Existence and stability of Xi -Hilfer fuzzy fractional? differential equation with boundary conditions

R. Vivek; D. Vivek; K. Kanagarajan; Elsayed M Elsayed

R. Vivek Department of Mathematics, \newline Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India
D. Vivek Department of Mathematics,\newline PSG College of Arts and Science , Coimbatore-641014, India
K. Kanagarajan Department of Mathematics, \newline Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.
Elsayed M Elsayed King Abdulaziz University

Abstract

The main objective of this paper is to study properties of ?-Hilfer fuzzy fractional di?erential equations which are useful in modeling variety of phenomena in physical sciences. The existence, uniqueness and stability of solutions are obtained. The technique used for study is fixed point theorem and Gronwall inequality. Ulam-Hyers-Rassias stability of the solution is also investigated.