ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

E$_{alpha }$-Ulam-Hyers Stability Result for $psi$-Hilfer Nonlocal Fractional Differential Equation

Discontinuity, Nonlinearity, and Complexity 10(2) (2021) 275--288 | DOI:10.5890/DNC.2021.06.008

Mohammed A. Almalahi , Satish K. Panchal

Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004 (M.S.), India

Abstract

In this paper we study the existence and uniqueness results of }$\psi${ -Hilfer nonlocal fractional differential equation with constant coefficient by using some properties of Mittag-Leffler function and fixed point theorems such as Banach and Schaefer's fixed point theorems. The generalized Gronwall inequality lemma is used in analyze E}$_{\alpha }${ -Ulam-Hyers stability. Finally, an example is provided to illustrate the obtained results.

Acknowledgments

The authors thank the referees for their careful reading of the manuscript and insightful comments, which helped to improve the quality of the paper. We would also like to acknowledge the valuable comments and suggestions from the editors, which vastly contributed to improve the presentation of the paper.

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