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

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...

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Bibliographic Details
Published in:Fractal and fractional 2024-08, Vol.8 (8), p.466
Main Authors: Martínez, Francisco, Kaabar, Mohammed
Format: Article
Language:English
Subjects:
Adomian Decomposition Method
Calculus
Decomposition
Fractals
fractal–fractional differentiation
fractal–fractional integral equations
fractal–fractional integration
Fractional calculus
Integral equations
Operators (mathematics)
Ordinary differential equations
Power
Volterra integral equations
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Summary: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.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8080466