arXiv subjects

Amar Chidouh

Publications and source records attributed to Amar Chidouh.

5 recordsLinked to original sources

arXiv2022

Study of a Fractional Creep Problem with Multiple Delays in Terms of Boltzmann's Superposition Principle

We study a class of nonlinear fractional differential equations with multiple delays, which is represented by the Voigt creep fractional model of viscoelasticity. We discuss two Voigt models, the first being linear and the second being nonlinear. The linear Voigt model give us the physical interpretation and is associated with important results since the creep function characterizes the viscoelastic behavior of stress and strain. For the nonlinear model of Voigt, our theoretical study and analysis provides existence and stability, where time delays are expressed in terms of Boltzmann's superposition principle. By means of the Banach contraction principle, we prove existence of a unique solution and investigate its continuous dependence upon the initial data as well as Ulam stability. The results are illustrated with an example.

math.AP↗

arXiv2022

Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space

We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel'skii fixed point theorem we prove, via the Kolmogorov--Riesz criteria, existence of solutions. The existence results are established in a specific fractional derivative Banach space and they are illustrated by two numerical examples.

math.CA↗

arXiv2017

Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities

We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.

math.CA↗

arXiv2016

Linear and nonlinear fractional Voigt models

We consider fractional generalizations of the ordinary differential equation that governs the creep phenomenon. Precisely, two Caputo fractional Voigt models are considered: a rheological linear model and a nonlinear one. In the linear case, an explicit Volterra representation of the solution is found, involving the generalized Mittag-Leffler function in the kernel. For the nonlinear fractional Voigt model, an existence result is obtained through a fixed point theorem. A nonlinear example, illustrating the obtained existence result, is given.

math.CA↗

arXiv2016

A generalized Lyapunov's inequality for a fractional boundary value problem

We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated through examples.

math.CA↗