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Latest Published Articles

A fixed point theorem for generalized weakly contractive mappings in \(b\)-metric spaces

OMS-Vol. 4 (2020), Issue 1, pp. 1 – 8 Open Access Full-Text PDF
Eliyas Zinab, Kidane Koyas, Aynalem Girma
Abstract: In this paper we establish a fixed point theorem for generalized weakly contractive mappings in the setting of \(b\)-metric spaces and prove the existence and uniqueness of a fixed point for a self-mappings satisfying the established theorem. Our result extends and generalizes the result of Cho [1]. Finally, we provided an example in the support of our main result.
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Existence of solution for a nonlinear fifth-order three-point boundary value problem

OMA-Vol. 3 (2019), Issue 2, pp. 125 – 136 Open Access Full-Text PDF
Zouaoui Bekri, Slimane Benaicha
Abstract: In this paper, we explore the existence of nontrivial solution for the fifth-order three-point boundary value problem of the form \(u^{(5)}(t)+f(t,u(t))=0,\quad\text 0<t<1,\) with boundary conditions \(u(0)=0,\quad u^{‘}(0)=u^{”}(0)=u^{”’}(0)=0,\quad u(1)=\alpha u(\eta),\) where \(0<\eta<1\), \(\alpha\in\mathbb{R}\), \(\alpha\eta^{4}\neq1\), \(f\in C([0,1]\times\mathbb{R},\mathbb{R})\). Under certain growth conditions on the non-linearity \(f\) and using Leray-Schauder nonlinear alternative, we prove the existence of at least one solution of the posed problem. Furthermore, the obtained results are further illustrated by mean of some examples.
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Existence and uniqueness results for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations

OMA-Vol. 3 (2019), Issue 2, pp. 106 – 111 Open Access Full-Text PDF
Abdelouaheb Ardjouni, Adel Lachouri, Ahcene Djoudi
Abstract: In this paper, we use the Banach fixed point theorem to obtain the existence, interval of existence and uniqueness of solutions for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations. We also use the generalization of Gronwall’s inequality to show the estimate of the solutions.
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New inequalities based on harmonic log-convex functions

OMA-Vol. 3 (2019), Issue 2, pp. 103 – 105 Open Access Full-Text PDF
Imran Abbas Baloch, Silvestru Sever Dragomir
Abstract: Harmonic convexity is very important new class of non-convex functions, it gained prominence in the Theory of Inequalities and Applications as well as in the rest of Mathematics’s branches. The harmonic convexity of a function is the basis for many inequalities in mathematics. Furthermore, harmonic convexity provides an analytic tool to estimate several known definite integrals like \(\int_{a}^{b} \frac{e^{x}}{x^{n}}dx\), \(\int_{a}^{b} e^{x^{2}} dx\), \(\int_{a}^{b} \frac{\sin x}{x^{n}}dx\) and \(\int_{a}^{b} \frac{\cos x}{x^{n}}dx\) \(\forall n \in \mathbb{N}\), where \(a,b \in (0,\infty)\). In this article, some un-weighted inequalities of Hermite-Hadamard type for harmonic log-convex functions defined on real intervals are given.
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The analysis of failure and reliability factors of impressed current cathodic protection (ICCP) design toward underwater line of warship (Case study in kri kcr-40 type)

EASL-Vol. 2 (2019), Issue 4, pp. 45 – 56 Open Access Full-Text PDF
Nengah Putra, Romie Oktovianus Bura, Sovian Aritonang, Djoko Navalino, Joni Widjayanto
Abstract: Corrosion at the bottom of a ship’s water line can result in personnel and material safety risks. There are 2 (two) ways to protect against corrosion, they are passive protection (by painting) and active protection (by cathodic protection method). In the KRI with KCR-40 type, the design of the bottom line of the ship’s waterline protection has been carried out with ICCP, but the value of its failure risk and reliability is unknown, both functional and designs, so that the design of the tool cannot be used maximally. This research aimed to determine the factors of failure and reliability value of the design-based ICCP (Reliability by Design) with the FTA and FMEA approach, the FTA aimed to identify the risks that contribute to the failure. The main factors causing failure in the design of ICCP tools occur in the component of Steel potential indicator and rectifier indicator with a failure mode not pointing to the correct number, this will result in corrosion control which is expected to be uncontrolled properly and correctly due to incorrect data input. After analyzing the FTA, the reliability value was 33%. Mitigation of tool components that have a high level of risk among other things in the indicator of steel potential and rectifier indicators: the first was to redesign the laying of some components of the tool compilers to pay attention to the circulating circulation in the box so that the tool works more optimally, the second was to carry out periodic control while the device was operating, and third was to ensure that the electrical power used was stable so there were no problems with the ICCP device while the ICCP device was operating.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC