<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this article we present the existence and uniqueness results for fractional integro-differential equations with <italic>ψ</italic>-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss <italic>E</italic><sub>α</sub> -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the <italic>δ</italic>-approximate solution.</p></abstract>

In this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

Existence results of <italic>ψ</italic>-Hilfer integro-differential equations with fractional order in Banach space

Dr Babasaheb Ambedkar Marathwada University

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Existence results of -Hilfer integro-differential equations with fractional order in Banach space

In this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The...

Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

Published Online: Dec 31, 2020

Page range: 171 - 192

Received: Feb 13, 2020

Accepted: May 23, 2020

DOI: https://doi.org/10.2478/aupcsm-2020-0013

Keywords
-Hilfer fractional derivative, Mönch fixed point theorem, -Ulam-Hyers stability, -approximate solution

© 2020 Mohammed A. Almalahi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

Published Online: Dec 31, 2020

Page range: 171 - 192

Received: Feb 13, 2020

Accepted: May 23, 2020

DOI: https://doi.org/10.2478/aupcsm-2020-0013

Keywords-Hilfer fractional derivative, Mönch fixed point theorem, -Ulam-Hyers stability, -approximate solution

© 2020 Mohammed A. Almalahi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
-Hilfer fractional derivative, Mönch fixed point theorem, -Ulam-Hyers stability, -approximate solution