Generalized solutions for time $\psi$-fractional evolution equations-Reference-Cited by-同舟云学术

Generalized solutions for time $\psi$-fractional evolution equations

Published:2024-06-03 Issue: Volume:42 Page:1-14
ISSN:2175-1188
Container-title:Boletim da Sociedade Paranaense de Matemática
language:
Short-container-title:B Soc Paran Mat

Author:

Benmerrous Abdelmjid^ORCID,Chadli Lalla saadia,Moujahid Abdelaziz,Elomari M'hamed^ORCID,Melliani Said^ORCID

Abstract

This paper focuses on the time fractional wave problem with the use of a new fractional derivative in Colombeau algebra. Using Banach's fixed point theorem and Laplace transforms, we give and prove the integral solution of the problem. In Colombeau's algebra, The existence and uniqueness of the solution are demonstrated using the Gronwall lemma.

Publisher

Sociedade Paranaense de Matemática

Reference25 articles.

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5. Benmerrous, A, Chadli,L. S, Moujahid, A, Elomari,M. H, and Melliani, S., "Solution of Non-homogeneous Wave Equation in Extended Colombeau Algebras", International Journal of Difference Equations (IJDE), 18(1), 107-118 (2023).