A robust scheme for Caputo variable-order time-fractional diffusion-type equations

Sadri, Khadijeh; Hosseini, K.; Băleanu, Dumitru; Salahshour, Soheil; Hinçal, Evren

doi:10.1007/s10973-023-12141-0

J Therm Anal Calorim

2023

DOI: 10.1007/s10973-023-12141-0

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A robust scheme for Caputo variable-order time-fractional diffusion-type equations

Khadijeh Sadri¹,

K. Hosseini²,

Dumitru Băleanu

et al.

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Cited by 12 publications

References 39 publications

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Bidimensional Gegenbauer Polynomials for Variable‐Order Time‐Fractional Integro‐Partial Differential Equation With a Weakly Singular Kernel

Yaghoubi,

Aminikhah,

Sadri

2024

Math Methods in App Sciences

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In this paper, a pseudo‐operational collocation method based on Gegenbauer polynomials is presented to solve a category of variable‐order time‐fractional integro‐partial differential equations with singular kernels. The applications of these functional equations can be revealed in the theory of elasticity, hydrodynamics, heat conduction, and nuclear reactor theory. The pseudo‐operational matrices are constructed utilizing bivariate Gegenbauer polynomials to approximate the solution of the mentioned equation. Then, using the collocation method and resultant matrices, the main equation is converted into a system of algebraic equations that can be solved by Newton's iteration method. Besides presenting a fast and accurate method, an error bound is determined in a Gegenbauer‐weighted space for the residual function obtained from the proposed approach. Finally, several test examples are performed to confirm the reliability and efficiency of the proposed method.

show abstract

Bidimensional Gegenbauer Polynomials for Variable‐Order Time‐Fractional Integro‐Partial Differential Equation With a Weakly Singular Kernel

Yaghoubi,

Aminikhah,

Sadri

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

The hyperbolic multi-term time fractional integro-differential equation with generalized Caputo derivative and error estimate in $$L_{p,\gamma ,\upsilon }$$ space

Azin,

Baghani,

Habibirad

2024

Z. Angew. Math. Phys.

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New Hermite collocation approach with shocks wave capturing for solving non-linear coupled Burgers-type model at high Reynolds number

Kumari,

Kumar,

Kukreja

2024

Engineering with Computers

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A robust scheme for Caputo variable-order time-fractional diffusion-type equations

Cited by 12 publications

References 39 publications

Bidimensional Gegenbauer Polynomials for Variable‐Order Time‐Fractional Integro‐Partial Differential Equation With a Weakly Singular Kernel

Bidimensional Gegenbauer Polynomials for Variable‐Order Time‐Fractional Integro‐Partial Differential Equation With a Weakly Singular Kernel

The hyperbolic multi-term time fractional integro-differential equation with generalized Caputo derivative and error estimate in $$L_{p,\gamma ,\upsilon }$$ space

New Hermite collocation approach with shocks wave capturing for solving non-linear coupled Burgers-type model at high Reynolds number

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