Abstract
In this paper, we study the existence of solutions for a new class of boundary value problems for nonlinear fractional differential inclusions with mixed type integral boundary conditions. The cases when the multifunction has convex as well as non-convex values are considered. Our results rely on the standard tools of fixed point theory and are well illustrated with the aid of an example.
Highlights
Introduction and preliminariesFractional differential equations and inclusions are generalizations of ordinary differential equations and inclusions to arbitrary non-integer orders
Many papers have been published about fractional differential equations and inclusions by researchers which apply the fixed point theory in their existence theorems
In [ ], it has been proved that the general solution of the fractional differential equation cDαu(t) = is given by u(t) = c + c t + c t + · · · + cn– tn, where c, . . . , cn– are real constants and n = [α] +
Summary
Introduction and preliminariesFractional differential equations and inclusions are generalizations of ordinary differential equations and inclusions to arbitrary non-integer orders. Many papers have been published about fractional differential equations and inclusions by researchers which apply the fixed point theory in their existence theorems. In [ ], it has been proved that the general solution of the fractional differential equation cDαu(t) = is given by u(t) = c + c t + c t + · · · + cn– tn– , where c , .
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