Dynamics and stability results for impulsive type integro-differential equations with generalized fractional derivative

Volume 4, Issue 1, pp 1--12 http://dx.doi.org/10.22436/mns.04.01.01

Publication Date: August 07, 2019 Submission Date: September 22, 2017 Revision Date: January 29, 2019 Accteptance Date: January 30, 2019

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Authors

D. Vivek - Department of Mathematics, P.S.G. College of Arts and Science, Coimbatore-641 014, India. E. M. Elsayed - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. K. Kanagarajan - Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641 020, India.

Abstract

In this paper, we investigate the existence, uniqueness, and Ulam stability of solutions for impulsive type integro-differential equations with generalized fractional derivative. The arguments are based upon the Banach contraction principle and Schaefer's fixed point theorem. \begin{keyword}Integro-differential equations \sep impulsive differential equations \sep generalized fractional derivative \sep existence \sep Ulam-Hyers stablity. \MSC{26A33\sep 34D10\sep 45N05.}

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Keywords

• Integro-differential equations
• impulsive differential equations
• generalized fractional derivative
• existence
• Ulam-Hyers stablity

MSC

•  26A33
•  34D10
•  45N05

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