Existence and Ulam-Hyers Mittag-Leffler stability of ψ-Hilfer fractional functional integrodifferential equation

2020/01/06 by Mohammed S. ‬Abdo, Abdo, Mohammed S., Abdulkafi Mohammed Saeed +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2001.01567

openalex publication_date 2020/01/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

This paper is committed to establishing the assumptions essential for the existence and uniqueness results of a fractional functional integrodifferential equation (FFIDE) having a derivative of generalized Hilfer type. Using the Picard operator method, and Banach fixed point theorem, we obtain the existence and uniqueness solution to the proposed problem. Along with this, the Ulam-Hyers Mittag-Leffler (UHML) stability is discussed via Pachpatte's inequality. For supporting our results, an illustrative example will be introduced.

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