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

Mohammed A. Almalahi; Satish K. Panchal

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2020)

  • Volume: 19, page 171-192
  • ISSN: 2300-133X

Abstract

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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.

How to cite

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Mohammed A. Almalahi, and Satish K. Panchal. "Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19 (2020): 171-192. <http://eudml.org/doc/296827>.

@article{MohammedA2020,
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.},
author = {Mohammed A. Almalahi, Satish K. Panchal},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {ψ-Hilfer fractional derivative; Mönch fixed point theorem; Eα-Ulam-Hyers stability; δ-approximate solution},
language = {eng},
pages = {171-192},
title = {Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space},
url = {http://eudml.org/doc/296827},
volume = {19},
year = {2020},
}

TY - JOUR
AU - Mohammed A. Almalahi
AU - Satish K. Panchal
TI - Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2020
VL - 19
SP - 171
EP - 192
AB - 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.
LA - eng
KW - ψ-Hilfer fractional derivative; Mönch fixed point theorem; Eα-Ulam-Hyers stability; δ-approximate solution
UR - http://eudml.org/doc/296827
ER -

References

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