Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative

Fahd Jarad; Sugumaran Harikrishnan; Kamal Shah; Kuppusamy Kanagarajan

doi:10.3934/dcdss.2020040

Article Contents

2020, Volume 13, Issue 3: 723-739. Doi: 10.3934/dcdss.2020040

This issue Previous Article Generalized fractional derivatives and Laplace transform Next Article Comparative study of fractional Fokker-Planck equations with various fractional derivative operators

Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative

1.
Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, 06790, Ankara, Turkey
2.
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India
3.
Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan

^* Corresponding author: Fahd Jarad
^* Corresponding author: Fahd Jarad

Received: May 2018

Published: December 2019

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Abstract

In this paper, the existence, uniqueness and stability of random implicit fractional differential equations (RIFDs) with nonlocal condition and impulsive effect involving a generalized Hilfer fractional derivative (HFD) are discussed. The arguments are discussed via Krasnoselskii's fixed point theorems, Schaefer's fixed point theorems, Banach contraction principle and Ulam type stability. Some examples are included to ensure the abstract results.

Keywords:

Random implicit differential equations,
generalized Hilfer fractional derivative,
existence,
uniqueness and stability.

Mathematics Subject Classification: Primary: 34A08, 34A09; Secondary: 37H10.

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References

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