Blow-up result for a plate equation with fractional damping and nonlinear source terms
OMA-Vol. 4 (2020), Issue 2, pp. 32 – 41 Open Access Full-Text PDF
Soh Edwin Mukiawa
Abstract: In this work, we consider a plate equation with nonlinear source and partially hinged boundary conditions. Our goal is to show analytically that the solution blows up in finite time. The background of the problem comes from the modeling of the downward displacement of suspension bridge using a thin rectangular plate. The result in the article shows that in the present of fractional damping and a nonlinear source such as the earthquake shocks, the suspension bridge is bound to collapse in finite time.
Existence and uniqueness for delay fractional differential equations with mixed fractional derivatives
OMA-Vol. 4 (2020), Issue 2, pp. 26 – 31 Open Access Full-Text PDF
Ahmed Hallaci, Hamid Boulares, Abdelouaheb Ardjouni
Abstract: Using the Krasnoselskii’s fixed point theorem and the contraction mapping principle we give sufficient conditions for the existence and uniqueness of solutions for initial value problems for delay fractional differential equations with the mixed Riemann-Liouville and Caputo fractional derivatives. At the end, an example is given to illustrate our main results.
Numerical analysis of a quasistatic contact problem for piezoelectric materials
OMA-Vol. 4 (2020), Issue 2, pp. 15 – 25 Open Access Full-Text PDF
Youssef Ouafik
Abstract: A frictional contact problem between a piezoelectric body and a deformable conductive foundation is numerically studied in this paper. The process is quasistatic and the material’s behavior is modelled with an electro-viscoelastic constitutive law. Contact is described with the normal compliance condition, a version of Coulomb’s law of dry friction, and a regularized electrical conductivity condition. A fully discrete scheme is introduced to solve the problem. Under certain solution regularity assumptions, we derive an optimal order error estimate. Some numerical simulations are included to show the performance of the method.
Certain results on starlike and convex functions
OMA-Vol. 4 (2020), Issue 2, pp. 1 – 14 Open Access Full-Text PDF
Pardeep Kaur, Sukhwinder Singh Billing
Abstract: Using the technique of differential subordination, we here, obtain certain sufficient conditions for starlike and convex functions. In most of the results obtained here, the region of variability of the differential operators implying starlikeness and convexity of analytic functions has been extended. The extended regions of the operators have been shown pictorially.
Numerical analysis of least squares and perceptron learning for classification problems
ODAM-Vol. 3 (2020), Issue 2, pp. 30 – 49 Open Access Full-Text PDF
Larisa Beilina
Abstract: This work presents study on regularized and non-regularized versions of perceptron learning and least squares algorithms for classification problems. The Fréchet derivatives for least squares and perceptron algorithms are derived. Different Tikhonov’s regularization techniques for choosing the regularization parameter are discussed. Numerical experiments demonstrate performance of perceptron and least squares algorithms to classify simulated and experimental data sets.
On the solution of fractional Riccati differential equations with variation of parameters method
EASL-Vol. 3 (2020), Issue 3, pp. 1 – 9 Open Access Full-Text PDF
Ehtasham Ul Haq, Mazhar Ali, Abdullah Saeed Khan
Abstract: In this paper, Variation of Parameters Method (VPM) is used to find the analytical solutions of non-linear fractional order quadratic Riccati differential equation. The given method is applied to initial value problems of the fractional order Riccati differential equations. The proposed technique has no discretization, linearization, perturbation, transformation, preventive suspicions and it is also free from Adomian,s polynomials. The obtained results are compare with analytical solutions by graphical and tabular form.
