Bivariate Chebyshev Polynomials of the Fifth Kind for Variable-Order Time-Fractional Partial Integro-Differential Equations With Weakly Singular Kernel
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Date
2021
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Publisher
Springer
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GOLD
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Abstract
The shifted Chebyshev polynomials of the fifth kind (SCPFK) and the collocation method are employed to achieve approximate solutions of a category of the functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for the numerical solution of the problem under study. The suggested method changes solving the VTFWSPIDE into the solution of a system of linear algebraic equations. Error bounds of the approximate solutions are obtained, and the application of the proposed scheme is examined on five problems. The results confirm the applicability and high accuracy of the method for the numerical solution of fractional singular partial integro-differential equations.
Description
Salahshour, Soheil/0000-0003-1390-3551; Sadri Khatouni, Khadijeh/0000-0001-6083-9527; Ahmadian, Ali/0000-0002-0106-7050
Keywords
Variable-Order Time-Fractional Weakly Singular Partial Integro-Differential Equations, Pseudo-Operational Matrix, Fifth-Kind Chebyshev Polynomials, Caputo Derivative, Riemann-Liouville Integral, Orthogonal polynomials, Mathematical analysis, Quantum mechanics, Caputo derivative, Convergence Analysis of Iterative Methods for Nonlinear Equations, Differential equation, Fifth-kind Chebyshev polynomials, Numerical Methods for Singularly Perturbed Problems, QA1-939, FOS: Mathematics, Pseudo-operational matrix, Variable-order time-fractional weakly singular partial integro-differential equations, Variable (mathematics), Anomalous Diffusion Modeling and Analysis, Collocation method, Numerical Analysis, Physics, Classical orthogonal polynomials, Chebyshev equation, Pure mathematics, Partial differential equation, Chebyshev iteration, Applied mathematics, Modeling and Simulation, Riemann–Liouville integral, Physical Sciences, Jacobi polynomials, Kernel (algebra), Nonlinear system, Chebyshev polynomials, Finite Difference Schemes, Mathematics, Ordinary differential equation, Algebraic equation, Riemann-Liouville integral, Numerical methods for integral equations, fifth-kind Chebyshev polynomials, Fractional derivatives and integrals, pseudo-operational matrix, Fractional partial differential equations, Integro-partial differential equations, variable-order time-fractional weakly singular partial integro-differential equations
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Sadri, Khadijeh...et al. (2021). "Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel", Advances in Difference Equations, Vol. 2021, No. 1.
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Q1
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OpenCitations Citation Count
14
Source
Advances in Difference Equations
Volume
2021
Issue
1
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Citations
CrossRef : 12
Scopus : 17
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