IMPULSIVE FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS IN BANACH SPACES
KAMALENDRA KUMAR *
Department of Mathematics, Shri Ram Murti Smarak College of Engineering and Technology, Bareilly-243001, India.
RAKESH KUMAR
Department of Mathematics, Hindu College, Moradabad-244001, India
*Author to whom correspondence should be addressed.
Abstract
In this paper, we study the existence of a mild solution of the nonlocal neutral fractional integrodifferential equations with impulsive conditions by using the probability density function. We obtain various criteria on the existence of mild solutions by using the semigroup theory and Sadovskii’s fixed point theorem. As an application controllability problem is studied for nonlocal neutral fractional integrodifferential equation with impulsive conditions.
Keywords: Fractional calculus, semigroup theory, mild solution;, nonlocal conditions, neutral fractional integrodifferential equations, Sadovskii’s fixed point theorem, Impulsive conditions.