Existence of mild solutions for nonlocal ψ−Caputo-type fractional evolution equations with nondense domain

The main crux of this manuscript is to establish the existence and uniqueness of solutions for nonlocal fractional evolution equations involving −Caputo fractional derivatives of an arbitrary order ∈ (0, 1) with nondense domain. The mild solutions of our proposed model are constructed by employing g...

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Bibliographic Details
Published in:Nonautonomous Dynamical Systems 2022-12, Vol.9 (1), p.272-289
Main Authors: Mfadel, Ali El, Melliani, Said, Kassidi, Abderrazak, Elomari, M’hamed
Format: Article
Language:English
Subjects:
26A33
34A08
34K37
Caputo fractional derivative
fractional integral
mild solution
ψ−caputo fractional derivative
ψ−fractional integral
ψ−mild solution
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Summary:The main crux of this manuscript is to establish the existence and uniqueness of solutions for nonlocal fractional evolution equations involving −Caputo fractional derivatives of an arbitrary order ∈ (0, 1) with nondense domain. The mild solutions of our proposed model are constructed by employing generalized −Laplace transform and some new density functions. The proofs are based on Krasnoselskii fixed point theorem and some basic techniques of −fractional calculus. As application, a nontrivial example is given to illustrate our theoritical results.
ISSN:2353-0626
2353-0626
DOI:10.1515/msds-2022-0157