An effective computational solver for fractal-fractional 2D integro-differential equations

Rahimkhani, P.; Sedaghat, S.; Ordokhani, Y.

doi:10.1007/s12190-024-02099-z

J. Appl. Math. Comput.

2024

DOI: 10.1007/s12190-024-02099-z

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An effective computational solver for fractal-fractional 2D integro-differential equations

P. Rahimkhani,

S. Sedaghat,

Y. Ordokhani

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A numerical method for Ψ-fractional integro-differential equations by Bell polynomials

Rahimkhani

2025

Applied Numerical Mathematics

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A numerical method for Ψ-fractional integro-differential equations by Bell polynomials

Rahimkhani

2025

Applied Numerical Mathematics

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

Martínez,

Kaabar

2024

Fractal Fract

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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.

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An effective computational solver for fractal-fractional 2D integro-differential equations

Cited by 2 publications

References 38 publications

A numerical method for Ψ-fractional integro-differential equations by Bell polynomials

A numerical method for Ψ-fractional integro-differential equations by Bell polynomials

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

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