"On the Explicit Solution of ψ-Hilfer Integro-Differential Nonlocal Cau" by Mohammed A. Almalahi, Satish K. Panchal et al.

Progress in Fractional Differentiation & Applications

Article Title

On the Explicit Solution of ψ-Hilfer Integro-Differential Nonlocal Cauchy Problem

Authors

Mohammed A. Almalahi, Department of Mathematics, Hajjah University, Hajjah, YemenFollow
Satish K. Panchal, Department of Mathematics, Dr.Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S),431001, IndiaFollow
Khaled Aldwoah, Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi ArabiaFollow
Mansour Lotayif, College of Administrative Sciences, Applied Science University, P.O. Box 5055, East Al-Ekir, Kingdom of BahrainFollow

Author Country (or Countries)

Yemen

Abstract

The point of this work is to analyze and investigate the suffcient conditions of the existence and uniqueness of explicit solution for ψ-Hilfer fractional differential equation (FDEs) with constant coefficient in the form of Mittag-Leffler (ML) function by using Holder inequality and two well-known fixed point theorems, namely Banach and Schaefer. Utilizing generalised Gronwall inequality lemma, Eκ -Ulam stability results is evaluated. Additionally, some examples are provided to demonstrate how our findings can be applied.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/090104

Recommended Citation

A. Almalahi, Mohammed; K. Panchal, Satish; Aldwoah, Khaled; and Lotayif, Mansour (2023) "On the Explicit Solution of ψ-Hilfer Integro-Differential Nonlocal Cauchy Problem," Progress in Fractional Differentiation & Applications: Vol. 9: Iss. 1, Article 4.
DOI: http://dx.doi.org/10.18576/pfda/090104
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol9/iss1/4

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