A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations

Abstract

This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach spaceX. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a concrete integrodifferential equation is obtained.

Existence and continuous dependence of mild solutions for impulsive fractional integrodifferential equations in Banach spaces

“…Recently, Li et al (2012) studied fractional integrodifferential equations of the type: (t, s, x(s)) ds)…”

Existence and uniqueness of solutions for nonlinear fractional integrodifferential equations with non-local boundary conditions

“…Moreover, nonlocal BVPs for fractional differential equations have gained significant observation (see [5], [30]) which consists of two ,three and multi point and nonlocal boundary value problems as special cases. see ([4], [10], [13], [17]).…”

Mild Solutions to the Cauchy Problem for Some Fractional Differential Equations with Delay

“…As shown in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein, differential equations with delay or differential equations of fractional order have appeared in many branches of science and technology. They have received a lot of attention in all these years.…”