Abstract
This note is concerned with establishing the existence of solutions to a fractional differential inclusion of a ψ-Caputo-type with a nonlocal integral boundary condition. Using the concept of the endpoint theorem for φ-weak contractive maps, we investigate the existence of solutions to the proposed problem. An example is provided at the end to clarify the theoretical result.
Highlights
1 Introduction On different time ranges, fractional calculus has had great impact due to a diversity of applications that have contributed to several fields of technical sciences and engineering [1,2,3,4,5]
The area of fractional-order differential inclusions has become mainly important as these equations were found to be of high importance in modeling stochastic and optimal controls problems [13]
We introduce some notations and definitions of fractional calculus with respect to another function and give preliminary results that we will need in our proofs later
Summary
Fractional calculus has had great impact due to a diversity of applications that have contributed to several fields of technical sciences and engineering [1,2,3,4,5]. We deal with the following ψ-fractional differential inclusions: cDψσ u(y) ∈ Z y, u(y) , y ∈ J = [1, T], 1 < σ ≤ 2, (1.1) We establish novel existence results of solutions for the above inclusion problem by using the endpoint theorem when the multivalued map is φ-weak contractive.
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