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EXISTENCE AND STABILITY RESULTS TO A CLASS OF FRACTIONAL RANDOM IMPLICIT DIFFERENTIAL EQUATIONS INVOLVING A GENERALIZED HILFER FRACTIONAL DERIVATIVE
Journal article   Open access  Peer reviewed

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 and Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India
Discrete and continuous dynamical systems. Series S, Vol.13(3), pp.723-739
2020
DOI: https://doi.org/10.3934/dcdss.2020040

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
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.
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https://doi.org/10.3934/dcdss.2020040View
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