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

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Abstract

The focus of this work is to construct a pseudo-operational Jacobi collocation scheme for numerically solving the Caputo variable-order time-fractional diffusion-type equations with applications in applied sciences. Modeling scientific phenomena in the context of fluid flow problems, curing reactions of thermosetting systems, solid oxide fuel cells, and solvent diffusion into heavy oils led to the appearance of these equations. For this reason, the numerical solution of these equations has attracted a lot of attention. More precisely, using pseudo-operational matrices and appropriate approximations based on bivariate Jacobi polynomials, the approximate solutions of the variable-order time-fractional diffusion-type equations in the Caputo sense with high accuracy are formally retrieved. Based on orthogonal bivariate Jacobi polynomials and their operational matrices, a sparse algebraic system is generated which makes implementing the proposed approach easy. An error bound is computed for the residual function by proving some theorems. To illustrate the accuracy and efficiency of the scheme, several illustrative examples are considered. The results demonstrate the efficiency of the present method compared to those achieved by the Legendre and Lucas multi-wavelet methods and the Crank-Nicolson compact method.

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Authors and Affiliations

  1. Department of Mathematics, Near East University TRNC, Mersin 10, 99138, Nicosia, Turkey

    Khadijeh Sadri, Kamyar Hosseini, Soheil Salahshour & Evren Hinçal

  2. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  3. Institute of Space Sciences, Magurele, Bucharest, R 76900, Romania

    Dumitru Baleanu

  4. Department of Medical Research, China Medical University, Taichung, 40447, Taiwan

    Dumitru Baleanu

  5. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    Soheil Salahshour

  6. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Soheil Salahshour

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  1. Khadijeh Sadri
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  2. Kamyar Hosseini
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  3. Dumitru Baleanu
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  4. Soheil Salahshour
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  5. Evren Hinçal
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Contributions

Authours’ contributions are as: Data curation, Formal analysis, Investigation, Methodology, Software, Writing-original draft by KS, Data curation, Resources, Validation, Writing-review & editing by KH, Resources, Supervision, Visualization, Writing-review & editing by DB, SS, EH. Authors declare that the study was carried out collaboratively with a division of responsibilities. All authors read and approved the final manuscript.

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Correspondence to Khadijeh Sadri or Dumitru Baleanu.

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Sadri, K., Hosseini, K., Baleanu, D. et al. A robust scheme for Caputo variable-order time-fractional diffusion-type equations. J Therm Anal Calorim 148, 5747–5764 (2023). https://doi.org/10.1007/s10973-023-12141-0

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