Annals of Mathematical Sciences and Applications

Volume 5 (2020)

Number 2

A study on random differential equations of arbitrary order

Pages: 141 – 169

DOI: https://dx.doi.org/10.4310/AMSA.2020.v5.n2.a1

Authors

K. Kanagarajan (Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India)

E. M. Elsayed (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia; and Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt)

S. Harikrishnan (Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.)

Abstract

In this paper, the well-posedness of fractional random differential equations (FRDEs) involving Hilfer-Katugampola fractional derivative (HKFD) is discussed. The sufficient conditions to existence of solutions for FRDEs involving initial, nonlocal and impulsive conditions are generated using standard fixed point theorems. Further the stability of solution is verified by the concept proposed by Ulam. Uniqueness solutions of initial value problems for FRDEs using picards iterative techique and continuous dependence of data are also discussed.

Keywords

random differential equations, Hilfer–Katugampola fractional derivative, well-posedness, stability

2010 Mathematics Subject Classification

26A33, 49K40, 93Exx

Full Text (PDF format)

Received 30 January 2020

Accepted 27 July 2020

Published 13 October 2020