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On Martínez–Kaabar Fractal–Fractional Volterra Integral Equations of the Second Kind

Authors :
Francisco Martínez
Mohammed K. A. Kaabar
Source :
Fractal and Fractional, Vol 8, Iss 8, p 466 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

The extension of the theory of generalized fractal–fractional calculus, named in this article as Martínez–Kaabar Fractal–Fractional (MKFF) calculus, is addressed to the field of integral equations. Based on the classic Adomian decomposition method, by incorporating the MKFF α,γ-integral operator, we establish the so-called extended Adomian decomposition method (EADM). The convergence of this proposed technique is also discussed. Finally, some interesting Volterra Integral equations of non-integer order which possess a fractal effect are solved via our proposed approach. The results in this work provide a novel approach that can be employed in solving various problems in science and engineering, which can overcome the challenges of solving various equations, formulated via other classical fractional operators.

Details

Language :
English
ISSN :
25043110
Volume :
8
Issue :
8
Database :
Directory of Open Access Journals
Journal :
Fractal and Fractional
Publication Type :
Academic Journal
Accession number :
edsdoj.709032a649484532bd6c7fbeab00f228
Document Type :
article
Full Text :
https://doi.org/10.3390/fractalfract8080466