<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

Publié en ligne: 31 déc. 2020

Pages: 171 - 192

Reçu: 13 févr. 2020

Accepté: 23 mai 2020

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

Mots clés
-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

Publié en ligne: 31 déc. 2020

Pages: 171 - 192

Reçu: 13 févr. 2020

Accepté: 23 mai 2020

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

Mots clés-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.

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