Abstract
In this paper, we study the existence of solutions for a new class of boundary value problems for nonlinear multi-term fractional differential inclusions. Our main result relies on the multi-valued form of Krasnoselskii’s fixed point theorem. An illustrative example is also presented.
Highlights
1 Introduction and preliminaries In this paper we study the existence of solutions for the following multi-term fractional differential inclusions: cDαu(t) ∈ F t, u(t), u (t), u (t), cDq u(t), . . . , cDqk u(t)
The Riemann-Liouville fractional order integral of the function u is defined by Iαu(t) =
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
1 Introduction and preliminaries In this paper we study the existence of solutions for the following multi-term fractional differential inclusions: cDαu(t) ∈ F t, u(t), u (t), u (t), cDq u(t), . Many of published papers about fractional differential equations and inclusions apply the fixed point theory for proving the existence results. 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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