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Implicit Fractional Differential Equation Involving $\psi$–Caputo with Boundary Conditions
by Boutiara Abdellatif   Maamar Benbachir

Vol. 16 No. 1 (2021) P.1~P.19
 DOI: https://doi.org/10.21915/BIMAS.2021101 10.21915/BIMAS.2021101

ABSTRACT

In this research article, we discuss the existence results and uniqueness of solutions for a class of boundary value problems of fractional differential equations with the $\psi$–Caputo fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii’s fixed point theorem. Besides, the Ulam-Hyers result is addressed for the proposed problem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes.

KEYWORDS
Implicit fractional differential equations, $\psi$–Caputo fractional derivative, fractional –integral, Ulam-Hyers stability, Boundary value problem, fixed point theorem

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 34B15, 34B18, 26A33, 34A12

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