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Novel Numerical Approach for Time Fractional Equations with Nonlocal Condition

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Abstract

A numerical method for solving inhomogeneous nonlocal time fractional convection-diffusion-reaction equations with variable coefficients has been developed. The fractional time operator is taken in the sense of the modified operator with the Mittag-Leffler kernel. The numerical method is based on the modified Gauss elimination with Taylor’s expansion. Through rigorous analysis, it has been proved that the given method is unconditionally stable and second-order convergent in space and time. The numerical results for three test problems illustrate the efficiency and validity of the theoretical estimates.

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Acknowledgements

The authors appreciate the helpful feedback and ideas from the anonymous reviewers. The first author is grateful to UGC, New Delhi, India (award letter No. 1282/(CSIR-UGC NET JUNE 2019)) for providing financial support, and the second author is thankful to CSIR, New Delhi, India (award letter No. 09/719(0096)/2019-EMR-I).

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031, India

    Komal Taneja, Komal Deswal & Devendra Kumar

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

    Dumitru Baleanu

  3. Institute of Space Science, Magurle-Bucharest, R-077125, Romania

    Dumitru Baleanu

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  1. Komal Taneja
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  2. Komal Deswal
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  3. Devendra Kumar
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  4. Dumitru Baleanu
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Correspondence to Komal Deswal.

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Taneja, K., Deswal, K., Kumar, D. et al. Novel Numerical Approach for Time Fractional Equations with Nonlocal Condition. Numer Algor 95, 1413–1433 (2024). https://doi.org/10.1007/s11075-023-01614-w

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  • DOI: https://doi.org/10.1007/s11075-023-01614-w

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