Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jaco...

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Bibliographic Details
Published inFractal and fractional Vol. 6; no. 1; p. 19
Main Authors Abdelkawy, Mohamed A., Amin, Ahmed Z. M., Lopes, António M., Hashim, Ishak, Babatin, Mohammed M.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2022
Subjects
Algorithms
Approximation
Boundary conditions
Collocation methods
Derivatives
Differential equations
Fractional calculus
fractional-order shifted Jacobi polynomial
Initial conditions
Integrals
Kernels
Polynomials
Riemann–Liouville fractional derivative
Riemann–Liouville fractional integral
variable-order fractional integro-differential equation
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ISSN2504-3110
2504-3110
DOI10.3390/fractalfract6010019

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Summary:We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract6010019