Abstract
This paper is devoted to study the existence of at least one continuous mild solution to semilinear fractional differential inclusion with deviated-advanced nonlocal conditions. We develop the results obtained, by exchanging the deviated-advanced nonlocal condition to an integral form. Our results will be accomplished by using the nonlinear Leray-Schauder’s alternative fixed point theorem. The main results are well illustrated with the aid of an example.
Highlights
In the last two decades, fractional differential equations have become one of the most important branches in mathematics, due to its wide range of applications in different fields of sciences and engineering, such as in physics, chemistry, and biology [1,2,3,4,5,6,7].Over the decades, a number of definitions of fractional derivatives are presented such as the most prevalent definitions of Riemann-Liouville and Caputo
Differential inclusions established as a part of the general theory of differential equations and penetrated different areas of sciences as a consequence of their numerous applications [8,9,10,11,12,13,14,15,16,17,18,19]
Many authors are interested in studying different classes of differential inclusions by using several forms of accompanying conditions
Summary
In the last two decades, fractional differential equations have become one of the most important branches in mathematics, due to its wide range of applications in different fields of sciences and engineering, such as in physics, chemistry, and biology [1,2,3,4,5,6,7].Over the decades, a number of definitions of fractional derivatives are presented such as the most prevalent definitions of Riemann-Liouville and Caputo. The aim of this paper is to discuss the existence of solutions to the following class of deviated-advanced nonlocal semilinear fractional differential inclusions cDαu(t) − A(t)u(t) ∈ F(t, u(t)), a.e, t ∈ J :=[ 0, T] , T < ∞; m k=1 ak u(φ (τk ))
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