Theoretical analysis and second-order approximation of solution of fractal-fractional differential equations with Mittag-Leffler Kernel

Some new uniqueness theorems are proposed and a flexible, efficient numerical algorithm is formulated and analysed for convergence and numerically verified for nonlinear fractal-fractional differential equations with Mittag-Leffler kernel. Under some generalized conditions which admit a wider class...

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Bibliographic Details
Published in:Mathematical and computer modelling of dynamical systems Vol. 30; no. 1; pp. 814 - 839
Main Authors: Atangana, Abdon, Nwaigwe, Chinedu
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 31.12.2024
Taylor & Francis Ltd
Taylor & Francis Group
Subjects:
Algorithms
Atangana-baleanu derivative
Convergence
Design standards
Differential equations
discrete gronwall inequlaity
experimental order of convergence
Fractal analysis
Fractional calculus
Lipschitz condition
Mathematical analysis
Numerical analysis
Smoothness
Uniqueness theorems
ISSN:1387-3954, 1744-5051
Online Access:Get full text
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Summary:Some new uniqueness theorems are proposed and a flexible, efficient numerical algorithm is formulated and analysed for convergence and numerically verified for nonlinear fractal-fractional differential equations with Mittag-Leffler kernel. Under some generalized conditions which admit a wider class of functions than the standard Lipschitz condition, the uniqueness of solution is established. By linearly interpolating between grid points, we design a numerical algorithm. Unlike existing methods, our constructed method avoids any form of grid restriction, uses minimal computation of special functions and is second order accurate under appropriate smoothness conditions. The convergence of the method is fully analysed, and numerical test cases are presented to verify the convergence result.
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ISSN:1387-3954
1744-5051
DOI:10.1080/13873954.2024.2417720