Generalized solutions of the Cauchy problem involving $\Phi$-Caputo fractional derivatives

The main objective of this research paper is to embed $\Phi$-Caputo fractional derivative in the Colombeau algebra of generalized functions and we investigate the existence and uniqueness of the Cauchy problem involving $\Phi$-Caputo fractional derivatives in the extended Colombeau algebras. Finally...

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Published inBoletim da Sociedade Paranaense de Matemática Vol. 42; pp. 1 - 12
Main Authors Taqbibt, Abdellah, El Bezdaoui, Latifa, Elomari, M'hamed, Chadli, Lalla Saadia
Format Journal Article
LanguageEnglish
Published Sociedade Brasileira de Matemática 21.05.2024
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Summary:The main objective of this research paper is to embed $\Phi$-Caputo fractional derivative in the Colombeau algebra of generalized functions and we investigate the existence and uniqueness of the Cauchy problem involving $\Phi$-Caputo fractional derivatives in the extended Colombeau algebras. Finally, we give anexample of how the ideas presented in the document can be applied.
ISSN:0037-8712
2175-1188
DOI:10.5269/bspm.66650