OMS – Vol 7 – 2023 – PISRT https://old.pisrt.org Mon, 01 Jan 2024 03:42:01 +0000 en-US hourly 1 https://wordpress.org/?v=6.7 Corrigenda to “The Galerkin method and hinged beam dynamics” https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/corrigenda-to-the-galerkin-method-and-hinged-beam-dynamics/ Fri, 29 Dec 2023 13:46:12 +0000 https://old.pisrt.org/?p=8237
OMS-Vol. 7 (2023), Issue 1, pp. 352-354 Open Access Full-Text PDF
David Raske
Abstract:This corrigenda makes seven corrections to D. Raske, "The Galerkin method and hinged beam dynamics," Open Journal of Mathematical Sciences 2023, 7, 236-247.]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 352-354
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0218

Corrigenda to “The Galerkin method and hinged beam dynamics”

David Raske
1210 Washtenaw, Ypsilanti, MI, 48197, USA.; nonlinear.problem.solver@gmail.com

Copyright © 2023 David Raske. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: November 9, 2023 – Published: December 29, 2023

Abstract

This corrigenda makes seven corrections to D. Raske, “The Galerkin method and hinged beam dynamics,” Open Journal of Mathematical Sciences 2023, 7, 236-247.

Keywords:

Nonlinear partial differential equations; Galerkin method; Continuum mechanics.
]]> Sun’s six conjectures on Apéry-like sums involving ordinary harmonic numbers https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/suns-six-conjectures-on-apery-like-sums-involving-ordinary-harmonic-numbers/ Wed, 27 Dec 2023 13:06:29 +0000 https://old.pisrt.org/?p=8216
OMS-Vol. 7 (2023), Issue 1, pp. 346-351 Open Access Full-Text PDF
Parth Chavan and Sarth Chavan
Abstract:The main goal of this brief article is to provide an elementary proof of Sun's six conjectures on Apéry-like sums involving ordinary harmonic numbers. ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 346-351
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0217

Sun’s six conjectures on Apéry-like sums involving ordinary harmonic numbers

Parth Chavan\(^{1,*}\), Sarth Chavan\(^{1}\)
\(^{1}\) Euler Circle, Palo Alto, CA 94306, USA.

Copyright © 2023 Parth Chavan and Sarth Chavan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 29, 2023 – Accepted: August 11, 2023 – Published: December 27, 2023

Abstract

The main goal of this brief article is to provide an elementary proof of Sun’s six conjectures on Apéry-like sums involving ordinary harmonic numbers.

Keywords:

Riemann zeta function; Catalans constant; Apéry-like sums; Harmonic numbers; Polylogarithm function; Polygamma function; Logarithmic integrals; Clausen function.
]]> Laplace transform method for logistic growth in a population and predator models with fractional order https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/laplace-transform-method-for-logistic-growth-in-a-population-and-predator-models-with-fractional-order/ Wed, 27 Dec 2023 12:57:44 +0000 https://old.pisrt.org/?p=8212
OMS-Vol. 7 (2023), Issue 1, pp. 339-345 Open Access Full-Text PDF
Abubker Ahmed
Abstract:In this paper, we develop a new application of the Laplace transform method (LTM) using the series expansion of the dependent variable for solving fractional logistic growth models in a population as well as fractional prey-predator models. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving fractional-order nonlinear differential equations. ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 339-345
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0216

Laplace transform method for logistic growth in a population and predator models with fractional order

Abubker Ahmed\(^{1,2,3*}\)
\(^{1}\)Ibn Khaldoon College, Program of Information Technology, Khartoum, Sudan.
\(^{2}\)AlMughtaribeen University, College of Engineering, Department of General Sciences, Sudan.
\(^{3}\)University of Science & Technology, College of Engineering, Sudan.

Copyright © 2023 Abubker Ahmed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: February 26, 2023 – Accepted: June 12, 2023 – Published: December 27, 2023

Abstract

In this paper, we develop a new application of the Laplace transform method (LTM) using the series expansion of the dependent variable for solving fractional logistic growth models in a population as well as fractional prey-predator models. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving fractional-order nonlinear differential equations.

Keywords:

Laplace transform method; Fractional power series; Caputo fractional derivative; Fractional differential equations.
]]> Establishment of Kifilideen coefficient tables for positive and negative powers of \(n\) and \(-n\) of Kifilideen trinomial theorem and other development based on matrix and standardized methods https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/establishment-of-kifilideen-coefficient-tables-for-positive-and-negative-powers-of-n-and-n-of-kifilideen-trinomial-theorem-and-other-development-based-on-matrix-and-standardized-methods/ Wed, 27 Dec 2023 12:54:12 +0000 https://old.pisrt.org/?p=8210
OMS-Vol. 7 (2023), Issue 1, pp. 325-338 Open Access Full-Text PDF
Kifilideen L. Osanyinpeju
Abstract:The generation of coefficients of terms of positive and negative powers of \(n\) and \(-n\) of Kifilideen trinomial theorem as the terms are progress is stressful and time-consuming which the same problem is identified with coefficients of terms of binomial theorem of positive and negative powers of \(n\) and \(-n\). This slows the process of producing the series of any particular trinomial expansion. This study established Kifilideen coefficient tables for positive and negative powers of \(n\) and \(-n\) of the Kifilideen trinomial theorem and other developments based on matrix and standardized methods. A Kifilideen theorem of matrix transformation of the positive power of \(n\) of trinomial expression in which three variables \(x,y\), and \(z\) are found in parts of the trinomial expression was originated. The development would ease evaluating the trinomial expression's positive power of \(n\). The Kifilideen coefficient tables are handy and effective in generating the coefficients of terms and series of the Kifilideen expansion of trinomial expression of positive and negative powers of \(n\) and \(-n.\) ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 325-338
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0215

Establishment of Kifilideen coefficient tables for positive and negative powers of \(n\) and \(-n\) of Kifilideen trinomial theorem and other development based on matrix and standardized methods

Kifilideen L. Osanyinpeju
\(^{1}\) Agricultural and Bio-Resources Engineering Department, College of Engineering, Federal University of Agriculture Abeokuta, Ogun State.

Copyright © 2023 Kifilideen L. Osanyinpeju. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: January 14, 2023 – Accepted: June 22, 2023 – Published: December 27, 2023

Abstract

The generation of coefficients of terms of positive and negative powers of \(n\) and \(-n\) of Kifilideen trinomial theorem as the terms are progress is stressful and time-consuming which the same problem is identified with coefficients of terms of binomial theorem of positive and negative powers of \(n\) and \(-n\). This slows the process of producing the series of any particular trinomial expansion. This study established Kifilideen coefficient tables for positive and negative powers of \(n\) and \(-n\) of the Kifilideen trinomial theorem and other developments based on matrix and standardized methods. A Kifilideen theorem of matrix transformation of the positive power of \(n\) of trinomial expression in which three variables \(x,y\), and \(z\) are found in parts of the trinomial expression was originated. The development would ease evaluating the trinomial expression’s positive power of \(n\). The Kifilideen coefficient tables are handy and effective in generating the coefficients of terms and series of the Kifilideen expansion of trinomial expression of positive and negative powers of \(n\) and \(-n.\)

Keywords:

Coefficients tables; Combination; Kifilideen matrix; Positive and negative powers; Kifilideen expansion.
]]> Measurable Taylor’s theorem: an elementary proof https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/measurable-taylors-theorem-an-elementary-proof/ Wed, 27 Dec 2023 12:36:22 +0000 https://old.pisrt.org/?p=8208
OMS-Vol. 7 (2023), Issue 1, pp. 321-324 Open Access Full-Text PDF
Gianluca Viggiano
Abstract:The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only tacitly assumed. In this note, we provide an elementary proof of this measurable Taylor's theorem, which guarantees that the interpolating point in the Lagrange form of the remainder can be chosen to depend measurably on the independent variable. ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 321-324
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0214

Measurable Taylor’s theorem: an elementary proof

Gianluca Viggiano\(^{1,*}\)
\(^{1}\) Bank of Italy, Regional Economic Research, Milan, Italy.

Copyright © 2023 Gianluca Viggiano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: July 10, 2023 – Accepted: August 11, 2023 – Published: December 27, 2023

Abstract

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor’s classical theorem is often needed, but only tacitly assumed. In this note, we provide an elementary proof of this measurable Taylor’s theorem, which guarantees that the interpolating point in the Lagrange form of the remainder can be chosen to depend measurably on the independent variable.

Keywords:

Trigonometric functions; Sinc function; Inequalities.
]]> On natural approaches related to classical trigonometric inequalities https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/on-natural-approaches-related-to-classical-trigonometric-inequalities/ Wed, 27 Dec 2023 12:27:17 +0000 https://old.pisrt.org/?p=8206
OMS-Vol. 7 (2023), Issue 1, pp. 299-320 Open Access Full-Text PDF
Abd Raouf Chouikha
Abstract:In this paper, we establish sharp inequalities for trigonometric functions. We prove in particular for \(0 < x < \frac{\pi}{2}\) and any \(n \geq 5\) \[0 < P_n(x)\ <\ (\sin x)^2- x^3\cot x < P_{n-1}(x) + \left[\left(\frac{2}{\pi}\right)^{2n} - \sum_{k=3}^{n-1} a_k \left(\frac{2}{\pi}\right)^{2n-2k}\right] x^{2n} \] where \(P_n(x) = \sum_{3=k}^n a_k x^{2k+1}\) is a \(n\)-polynomial, with positive coefficients (\(k \geq 5\)), \(a_{{k}}=\frac{{2}^{2\,k-2}}{\ \left( 2\,k-2 \right) ! } \left( \left| {B}_{ 2\,k-2} \right| +{\frac { \left( -1\right) ^{k+1}}{ \left( 2\,k-1 \right) k}} \right),\) \( B_{2k} \) are Bernoulli numbers. This improves a lot of lower bounds of \( \frac{\sin(x)}{x}\) and generalizes inequalities chains. Moreover, bounds are obtained for other trigonometric inequalities as Huygens and Cusa inequalities as well as for the function \[g_n(x) = \left(\frac{\sin(x)}{x}\right)^2 \left( 1 - \frac{2\left(\frac{2 x}{\pi}\right)^{2n+2}}{1-(\frac{2x}{\pi})^2}\right) +\frac{\tan(x)}{x}, \ n\geq 1 \]. ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 299-320
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0213

On natural approaches related to classical trigonometric inequalities

Abd Raouf Chouikha\(^{1,*}\)
\(^{1}\) 4, Cour des Quesblais 35430 Saint-Pere, FRANCE.

Copyright © 2023 Abd Raouf Chouikha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 24, 2023 – Accepted: September 24, 2023 – Published: December 27, 2023

Abstract

In this paper, we establish sharp inequalities for trigonometric functions. We prove in particular for \(0 < x < \frac{\pi}{2}\) and any \(n \geq 5\) \[0 < P_n(x)\ <\ (\sin x)^2- x^3\cot x < P_{n-1}(x) + \left[\left(\frac{2}{\pi}\right)^{2n} – \sum_{k=3}^{n-1} a_k \left(\frac{2}{\pi}\right)^{2n-2k}\right] x^{2n} \] where \(P_n(x) = \sum_{3=k}^n a_k x^{2k+1}\) is a \(n\)-polynomial, with positive coefficients (\(k \geq 5\)), \(a_{{k}}=\frac{{2}^{2\,k-2}}{\ \left( 2\,k-2 \right) ! } \left( \left| {B}_{ 2\,k-2} \right| +{\frac { \left( -1\right) ^{k+1}}{ \left( 2\,k-1 \right) k}} \right),\)
\( B_{2k} \) are Bernoulli numbers. This improves a lot of lower bounds of \( \frac{\sin(x)}{x}\) and generalizes inequalities chains.
Moreover, bounds are obtained for other trigonometric inequalities as Huygens and Cusa inequalities as well as for the function
\[g_n(x) = \left(\frac{\sin(x)}{x}\right)^2 \left( 1 – \frac{2\left(\frac{2 x}{\pi}\right)^{2n+2}}{1-(\frac{2x}{\pi})^2}\right) +\frac{\tan(x)}{x}, \ n\geq 1 \].

Keywords:

Trigonometric functions; Sinc function; Inequalities.
]]> Exploiting quadratic \(\varphi(\delta_{1},\delta_{2})-\)function inequalities on fuzzy Banach spaces based on general quadratic equations with \(2k\)-variables https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/exploiting-quadratic-varphidelta_1delta_2-function-inequalities-on-fuzzy-banach-spaces-based-on-general-quadratic-equations-with-2k-variables/ Wed, 27 Dec 2023 12:22:46 +0000 https://old.pisrt.org/?p=8204
OMS-Vol. 7 (2023), Issue 1, pp. 287-298 Open Access Full-Text PDF
Ly Van An
Abstract:In this manuscript, our primary focus revolves around extending the inequalities associated with the Quadratic \(\varphi(\delta_{1},\delta_{2})-\)function. Our approach involves leveraging the general quadratic functional equation encompassing \(2k\)-variables within the context of the fuzzy Banach space. Our main contribution lies in the expansion of these inequalities, representing a significant result within this study. ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 287-298
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0212

Exploiting quadratic \(\varphi(\delta_{1},\delta_{2})-\)function inequalities on fuzzy Banach spaces based on general quadratic equations with \(2k\)-variables

Ly Van An\(^{1,*}\)
\(^{1}\) Faculty of Mathematics Teacher Education, Tay Ninh University, Tay Ninh, Vietnam.

Copyright © 2023 Ly Van An. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: June 28, 2023 – Accepted: October 11, 2023 – Published: December 27, 2023

Abstract

In this manuscript, our primary focus revolves around extending the inequalities associated with the Quadratic \(\varphi(\delta_{1},\delta_{2})-\)function. Our approach involves leveraging the general quadratic functional equation encompassing \(2k\)-variables within the context of the fuzzy Banach space. Our main contribution lies in the expansion of these inequalities, representing a significant result within this study.

Keywords:

Generalized quadratic type \(\varphi(\delta_{1},\delta_{2})-\)functional inequality; Generalized quadratic type functional equations; Fuzzy Banach space; Fuzzy normed vector spaces.
]]> Some arguments for the wave equation in quantum theory 4 https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/some-arguments-for-the-wave-equation-in-quantum-theory-4/ Wed, 27 Dec 2023 12:17:42 +0000 https://old.pisrt.org/?p=8202
OMS-Vol. 7 (2023), Issue 1, pp. 279-286 Open Access Full-Text PDF
Tristram de Piro
Abstract:We classify particle paths for systems in thermal equilibrium satisfying the usual relations and prove that the only solutions are given by straight line parallel paths with speed \(c\). ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 279-286
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0211

Some arguments for the wave equation in quantum theory 4

Tristram de Piro\(^{1,*}\)
\(^{1}\) Flat 3, Redesdale House, 85 The Park, Cheltenham, GL50 2RP; t.depiro@curvalinea.net.

Copyright © 2023 Tristram de Piro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 18, 2023 – Accepted: August 11, 2023 – Published: December 27, 2023

Abstract

We classify particle paths for systems in thermal equilibrium satisfying the usual relations and prove that the only solutions are given by straight line parallel paths with speed \(c\).

Keywords:

Wave equation; Continuity equation; Maxwell’s equations; Jefimenko’s equations; Radiation.
]]> Modelling the dynamics of multi-strain COVID-19 transmission https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/modelling-the-dynamics-of-multi-strain-covid-19-transmission/ Wed, 08 Nov 2023 11:41:53 +0000 https://old.pisrt.org/?p=8139
OMS-Vol. 7 (2023), Issue 1, pp. 269-278 Open Access Full-Text PDF
Joel N. Ndam and Stephen T. Agba
Abstract: It is on record that rolling out COVID-19 vaccines has been one of the fastest for any vaccine production worldwide. Despite this prompt action taken to mitigate the transmission of COVID-19, the disease persists. One of the reasons for the persistence of the disease is that the vaccines do not confer immunity against the infections. Moreover, the virus-causing COVID-19 mutates, rendering the vaccines less effective on the new strains of the disease. This research addresses the multi-strains transmission dynamics and herd immunity threshold of the disease. Local stability analysis of the disease-free steady state reveals that the pandemic can be contained when the basic reproduction number, \(R_{0}\) is brought below unity. The results of numerical simulations also agree with the theoretical results. The herd immunity thresholds for some of the vaccines against COVID-19 were computed to guide the management of the disease. This model can be applied to any strain of the disease. ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 269-278
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0210

Modelling the Dynamics of Multi-strain COVID-19 Transmission

Joel N. Ndam\(^{1,}\)* and Stephen T. Agba\(^{2}\)
\(^{1}\) Department of Mathematics, University of Jos, Nigeria; ndamj@unijos.edu.ng
\(^{2}\) Department of Mathematics and Computer Science, Federal University of Health Sciences, Otukpo, Nigeria

Copyright © 2023 Joel N. Ndam and Stephen T. Agba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 18, 2023 – Accepted: August 11, 2023 – Published: November 08, 2023

Abstract

It is on record that rolling out COVID-19 vaccines has been one of the fastest for any vaccine production worldwide. Despite this prompt action taken to mitigate the transmission of COVID-19, the disease persists. One of the reasons for the persistence of the disease is that the vaccines do not confer immunity against the infections. Moreover, the virus-causing COVID-19 mutates, rendering the vaccines less effective on the new strains of the disease. This research addresses the multi-strains transmission dynamics and herd immunity threshold of the disease. Local stability analysis of the disease-free steady state reveals that the pandemic can be contained when the basic reproduction number, \(R_{0}\) is brought below unity. The results of numerical simulations also agree with the theoretical results. The herd immunity thresholds for some of the vaccines against COVID-19 were computed to guide the management of the disease. This model can be applied to any strain of the disease. .

Keywords:

Strain; Multi-strain; Vaccine; Vccine efficiency; Herd immunity; Normalised sensitivity index.
]]> Results on the growth of solutions of complex linear differential equations with meromorphic coefficients https://old.pisrt.org/psr-press/journals/oms-vol-7-2023/results-on-the-growth-of-solutions-of-complex-linear-differential-equations-with-meromorphic-coefficients/ Wed, 08 Nov 2023 11:16:21 +0000 https://old.pisrt.org/?p=8129
OMS-Vol. 7 (2023), Issue 1, pp. 248-268 Open Access Full-Text PDF
Mansouria Saidani and Benharrat Belaïdi
Abstract:The purpose of this paper is the study of the growth of solutions of higher order linear differential equations \(f^{\left( k\right) }+\left( A_{k-1,1}\left( z\right) e^{P_{k-1}\left(z\right) }+A_{k-1,2}\left( z\right) e^{Q_{k-1}\left( z\right) }\right)f^{\left( k-1\right) }+\cdots +\left( A_{0,1}\left( z\right) e^{P_{0}\left( z\right) }+A_{0,2}\left( z\right) e^{Q_{0}\left( z\right) }\right) f=0\) and \(f^{\left( k\right) }+\left( A_{k-1,1}\left( z\right) e^{P_{k-1}\left(z\right) }+A_{k-1,2}\left( z\right) e^{Q_{k-1}\left( z\right) }\right)f^{\left( k-1\right) }+\cdots +\left( A_{0,1}\left( z\right) e^{P_{0}\left( z\right)}+A_{0,2}\left( z\right) e^{Q_{0}\left( z\right) }\right) f=F\left( z\right),\) where \(A_{j,i}\left( z\right) \left( \not\equiv 0\right) \left(j=0,...,k-1;i=1,2\right) ,\) \(F\left( z\right) \) are meromorphic functions of finite order and \(P_{j}\left( z\right) ,Q_{j}\left( z\right) \) \((j=0,1,...,k-1;i=1,2)\) are polynomials with degree \(n\geq 1\). Under some others conditions, we extend the previous results due to Hamani and Belaïdi [1]. ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 248-268
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0209

Results on the growth of solutions of complex linear differential equations with meromorphic coefficients

Mansouria Saidani\(^{1,*}\), and Benharrat Belaïdi\(^1\)
\(^{1}\) Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem-(Algeria)

Copyright © 2023 Mansouria Saidani and Benharrat Belaïdi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 03, 2023 – Accepted: April 30, 2023 – Published: November 08, 2023

Abstract

The purpose of this paper is the study of the growth of solutions of higher order linear differential equations \(f^{\left( k\right) }+\left( A_{k-1,1}\left( z\right) e^{P_{k-1}\left(z\right) }+A_{k-1,2}\left( z\right) e^{Q_{k-1}\left( z\right) }\right)f^{\left( k-1\right) }+\cdots +\left( A_{0,1}\left( z\right) e^{P_{0}\left( z\right)
}+A_{0,2}\left( z\right) e^{Q_{0}\left( z\right) }\right) f=0\) and \(f^{\left( k\right) }+\left( A_{k-1,1}\left( z\right) e^{P_{k-1}\left(z\right) }+A_{k-1,2}\left( z\right) e^{Q_{k-1}\left( z\right) }\right)f^{\left( k-1\right) }+\cdots +\left( A_{0,1}\left( z\right) e^{P_{0}\left( z\right)}+A_{0,2}\left( z\right) e^{Q_{0}\left( z\right) }\right) f=F\left( z\right),\) where \(A_{j,i}\left( z\right) \left( \not\equiv 0\right) \left(j=0,…,k-1;i=1,2\right) ,\) \(F\left( z\right) \) are meromorphic functions of finite order and \(P_{j}\left( z\right) ,Q_{j}\left( z\right) \) \((j=0,1,…,k-1;i=1,2)\) are polynomials with degree \(n\geq 1\). Under some others conditions, we extend the previous results due to Hamani and Belaïdi [1].

Keywords:

Order of growth; Hyper-order; Exponent of convergence of zero sequence; Differential equation; Meromorphic function
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