Existence and multiplicity of solutions to an abstract Cauchy problem for an evolution equation involving fractional dissipation term of Caputo type

Nourredine Houari; Svetlin Georgiev  Georgiev; Abdelhamid  Hallouz; Hocine Mohamed  Braiki

doi:10.24193/subbmath.2025.4.09

Authors

Nourredine Houari Department of Mathematics and Computer Science, Faculty of Science and Technology, Tissemsilt University, Algeria https://orcid.org/0009-0001-2006-1420
Svetlin Georgiev Georgiev Department of Mathematics, Sorbonne University, Paris, France https://orcid.org/0000-0001-8015-4226
Abdelhamid Hallouz Department of Mathematics, Faculty of Mathematics and Computer Science, Tiaret University, Algeria https://orcid.org/0009-0007-1272-032X
Hocine Mohamed Braiki Department of Mathematics, Faculty of Mathematics and Computer Science, Tiaret University, Algeria https://orcid.org/0009-0003-2104-7908

DOI:

https://doi.org/10.24193/subbmath.2025.4.09

Keywords:

evolution equation, fractional derivative, fixed point theorem, existence, multiplicity

Abstract

The aim of this work is to investigate the existence and multiplicity of solutions to a nonhomogenious quasi-linear second order evolution equation involving a fractional dissipation term of Caputo type in abstract framework. Some Criteria on the existence of at least one or two solutions are obtained by using some well known fixed point theorems for the sum of two operators. An example is presented to validate our analysis.

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