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1

Numerical solution of a fractional coupled system with the Caputo-Fabrizio fractional derivative

Mansouri Ikram, Bekkouche Mohammed Moumen, Ahmed Abdelaziz Azeb

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 1

46--56

EN

Within this work, we discuss the existence of solutions for a coupled system of linear fractional differential equations involving Caputo-Fabrizio fractional orders. We prove the existence and uniqueness of the solution by using the Picard-Lindel ̈of method and fixed point theory. Also, to compute an approximate solution of problem, we utilize the Adomian decomposition method (ADM), as this method provides the solution in the form of a series such that the infinite series converge to the exact solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method.

2

Extremal solutions to a coupled system of nonlinear fractional differential equations with ψ–Caputo fractional derivatives

Derbazi Choukri, Baitiche Zidane, Benchohra Mouffak, Graef John R.

Journal of Mathematics and Applications

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2021

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Vol. 44

19--34

EN

Using the well-known monotone iterative technique together with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of coupled systems of nonlinear fractional differential equations involving the ψ–Caputo derivative with initial conditions. As applications of this work, two illustrative examples are presented.

3

Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations

Mustafa Muhammad I., Kafini Mohammad

Journal of Applied Analysis

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2019

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Vol. 25, nr 1

97--110

EN

In this paper, we consider a nonlinear quasilinear system of two coupled viscoelastic equations and investigate the asymptotic behavior of this system. We establish an explicit and general formula for the energy decay rates. Our result allows a wider class of relaxation functions, which improves earlier results existing in the literature.

4

Solvability of a Coupled System of Fractional Differential Equations with Nonlocal and Integral Boundary Conditions

Ahmad B., Ntouyas S. K., Alsaedi A., Hobiny A.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

91--108

EN

This paper is concerned with the existence and uniqueness of solutions for a coupled system of fractional differential equations with nonlocal and integral boundary conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. The results are explained with the aid of examples. The case of nonlocal strip conditions is also discussed.

5

On the weak solutions of a coupled system of Volterra-Stieltjes integral equations

El-Sayed A. M. A., Al-Fadel M. M. A.

Commentationes Mathematicae

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2017

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Vol 57, No. 2

143--151

EN

We present an existence theorem for at least one weak solution to a coupled system of Volterra-Stieltjes integral equations in a reflexive Banach space.

6

Flexural vibration of coupled double-walled Carbon nanotubes conveying fluid under thermo-magnetic fields based on strain gradient theory

Ghorbanpour Arani A., Dashti P., Amir S., Yousefi M.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 4

947--957

EN

The flexural vibration stability of a coupled double-walled viscoelastic carbon nanotube conveying a fluid based on the Timoshenko beam (TB) model is investigated. The coupled system is surrounded by an elastic medium which is simulated as Pasternak foundation. Van der Waals (vdW) forces between the inner and outer CNTs are taken into account based on the Lenard-Jones model. Using small scale theories, Hamilton’s principle and applying two dimensional (2D) magnetic field higher order governing equations are derived. The differential quadrature method (DQM) is applied to solve partial differential equations and investigate natural frequency of the system. The effects of viscoelastic constant, magnetic field with variable magnitudes and surface stresses on natural frequency of the structure are demonstrated in this study.

7

A coupled system of fractional order integral equations in reflexive Banach spaces

El-Sayed A.M.A., Hashem H.H.G.

Commentationes Mathematicae

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2012

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Vol. 52, [Z] 1

21-28

EN

We present an existence theorem for at least one weak solution for a coupled system of integral equations of fractional order in reflexive Banach spaces relative to the weak topology.