Existence of Mild Solution for Mixed Volterra–Fredholm Integro Fractional Differential Equation with Non-instantaneous Impulses
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We establish a set of sufficient conditions for the existence of mild solution of a class of fractional mixed integro differential equation with not instantaneous impulses. The results are obtained by establishing two theorems by using semigroup theory, Banach fixed point theorem and Krasnoselskii’s fixed point theorem. Two examples are presented to validate the results of the theorems.
KeywordsMild solution Fractional differential equation Impulse Banach fixed point theorem Krasnoselskii’s fixed point theorem
The first author is grateful to North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh, India for granting leave for three years to pursue PhD and to Indian Institute of Technology Guwahati, Guwahati, India for providing opportunity to carry out research. Both authors express their gratitude to the esteemed reviewers for their careful reading of the manuscript and the insightful comments, and also to the Editor for allowing revision of the manuscript which has now definitely reached a much better form.