Abstract
Abstract In this paper, a new existence result is obtained for a fractional multivalued problem with fractional integral boundary conditions by applying a (Krasnoselskii type) fixed-point result for multivalued maps due to Petryshyn and Fitzpatric [Trans. Am. Math. Soc. 194:1-25, 1974]. The case for lower semi-continuous multivalued maps is also discussed. An example for the illustration of our main result is presented. MSC:34A60, 34A08.
Highlights
The theory of fractional differential equations and inclusions has developed into an important field of investigation due to its extensive applications in numerous branches of physics, economics, and engineering sciences [ – ]
The nonlocal behavior exhibited by a fractional-order differential operator makes it distinct from the integer-order differential operator
Differential equations of arbitrary order are capable of describing memory and hereditary properties of several materials and processes
Summary
The theory of fractional differential equations and inclusions has developed into an important field of investigation due to its extensive applications in numerous branches of physics, economics, and engineering sciences [ – ]. For any h ∈ C( , ) ∩ L( , ), the unique solution of the linear fractional boundary value problem A multivalued map F : [ , ] × R → Pcp,c(R) is said to be L -Carathéodory if (i) t → F(t, x) is measurable for each x ∈ R, (ii) x → F(t, x) is upper semi-continuous for almost all t ∈ [ , ], and (iii) for each real number ρ > , there exists a function hρ ∈ L ([ , ], R+) such that
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