Fractional operators with Kaniadakis logarithm kernels

Authors

DOI:

https://doi.org/10.22481/intermaths.v3i1.10862

Keywords:

Fractional Integrals, Fractional Derivatives, Kaniadakis deformed logarithm

Abstract

In this article, more general types of fractional operators with κ-deformed logarithm kernels are proposed. We analyse the new operators and prove various facts about them, including a semi group property. Results of existence are established in appropriate functional spaces. We prove that these results are valid at once for several standard fractional operators such as the Riemann-Liouville and Caputo operators, the Hadamard operators depending on the of the scaling function. We also show that our technique can beuseful to solve a wide range of Volterra integral equations. Finally, the solutions of theκ-fractional differential equations can be deduced from the solution representation of theCaputo or Riemann-Liouville versions via scaling.

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Author Biographies

Ana Paula Perovano, State University of Southwest Bahia, Vitória da Conquista, BA 45083-900, Brazil

Doutoranda em Educação Matemática (UNESP). Mestre em Educação Matemática (PUC-SP). Professora da Universidade Estadual do Sudoeste da Bahia (UESB). Integrante do Grupo de Pesquisa TeorEMa - Interlocuções entre Geometria e Educação Matemática. Desenvolve estudos e pesquisas sobre Formação de Professores, Livros Didáticos de Matemática e Processos de Ensino e deAprendizagem da Matemática.

Fernando Santos Silva, Department of Exact and Technological Sciences, State University of Southwest Bahia, Vitória da Conquista, BA 45083-900, Brazil

Doutor em Modelagem Computacional e Tecnologia Industrial pelo Centro Universitário SENAI CIMATEC (Brasil). Pesquisa e desenvolve estudos sobre Cálculo Fracionário, Análise Funcional e Equações Integrodiferenciais Fracionárias.

References

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Published

2022-06-30

How to Cite

Perovano, A. P. ., & Silva, F. S. (2022). Fractional operators with Kaniadakis logarithm kernels. INTERMATHS, 3(1), 37-49. https://doi.org/10.22481/intermaths.v3i1.10862

Issue

Vol. 3 No. 1 (2022)

Section

Artigos

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