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On nonlinear fractional neutral differential equation with the ψ-Caputo fractional derivative

Nabil Tamer

Journal of Mathematics and Applications

2020

Vol. 43

99--112

In this article, the solvability of fractional neutral differential equation involving ψ-Caputo fractional operator is considered usinga Krasnoselskii’s fixed point approach. Also, we establish the uniquenessof the solution under certain conditions. Ulam stabilities for the proposedproblem are discussed. Finally, examples are displayed to aid the applicability of the theory results.

Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Benchohra Mouffak, Bouriah Soufyane, Nieto Juan J.

Demonstratio Mathematica

2019

Vol. 52, nr 1

437--450

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

Some new existence results and stability concepts for fractional partial random differential equations

Abbas S., Benchohra M., Darwish M. A.

Journal of Mathematics and Applications

2016

Vol. 39

5--22

In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.

Ulam stabilities for the Darboux problem for partial fractional differential inclusions

Abbas S., Benchohra M.

Demonstratio Mathematica

2014

Vol. 47, nr 4

826--838

In this article, we investigate some Ulam’s type stability concepts for the Darboux problem of partial fractional differential inclusions with a nonconvex valued right hand side. Our results are based upon Covitz-Nadler fixed point theorem and fractional version of Gronwall’s inequality.