Existence of mild solutions for fractional differential equations in separable Banach space

Abstract

This paper is concerned with the existence of mild solutions for fractional semilinear differential equations with non local conditions in separable Banach spaces. The result is established by using the technique of measures of noncompactness in Banach spaces of continuous functions and Schauder fixed point theorem. (2010): 34G20, 35R10. Mathematics subject classification

Strong and mild solutions of the system of fractional ordinary differential equation and it's applications

“…Zufeng Zhang, Bin Liu established sufficient conditions for the existence of mild solution of fractional differential evolution equation by using Banach fixed point theorem [14]. H.L.Tidke, M.B.Dhakne prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra-integro differential equations with non-local condition, and analysis is based on semigroup theory and Banach fixed point theorem [1,3]. Adel Jawahdow is concerned with the existence of mild solutions for fractional semilinear differential equations with non-local conditions in separable Banach space and furthermore the result is obtained using the technique of measures of non-compactness in Banach space of continuous functions and Schauder fixed point theorem [1].…”

“…H.L.Tidke, M.B.Dhakne prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra-integro differential equations with non-local condition, and analysis is based on semigroup theory and Banach fixed point theorem [1,3]. Adel Jawahdow is concerned with the existence of mild solutions for fractional semilinear differential equations with non-local conditions in separable Banach space and furthermore the result is obtained using the technique of measures of non-compactness in Banach space of continuous functions and Schauder fixed point theorem [1]. K.Bhalchandran, S. Ilamaran prove the existence and uniqueness of mild and strong solutions of a semilinear evolution equation with non-local initial conditions using method of semigroups and Banach fixed point theorem [5].…”