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Finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms

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  • Kumar, Kamlesh
  • Pandey, Rajesh K.
  • Yadav, Swati

Abstract

In this paper, a finite difference scheme is presented for the Generalized Time-Fractional Telegraph Equation (GTFTE) defined using Generalized Fractional Derivative (GFD) terms introduced recently. The generalization of fractional derivatives is done by introducing scale and weight functions, and for their particular choices, GFD reduces to Caputo and Riemann–Liouville derivatives. We present the solution behaviour of the GTFTE by changing the weight and scale functions in GFD. The convergence and the stability of the finite difference scheme (FDS) are also presented, and for the numerical simulation of the FDS, we consider examples which validate our numerical method.

Suggested Citation

  • Kumar, Kamlesh & Pandey, Rajesh K. & Yadav, Swati, 2019. "Finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    • Handle: RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119313081
    DOI: 10.1016/j.physa.2019.122271
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    References listed on IDEAS

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    1. Yadav, Swati & Pandey, Rajesh K. & Shukla, Anil K., 2019. "Numerical approximations of Atangana–Baleanu Caputo derivative and its application," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 58-64.
    2. Sun, HongGuang & Chen, Wen & Li, Changpin & Chen, YangQuan, 2010. "Fractional differential models for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2719-2724.
    3. Sharifi, Shokofeh & Rashidinia, Jalil, 2016. "Numerical solution of hyperbolic telegraph equation by cubic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 28-38.
    4. Arqub, Omar Abu & Maayah, Banan, 2018. "Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 117-124.
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    Cited by:

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    2. Yadav, Swati & Pandey, Rajesh K., 2020. "Numerical approximation of fractional burgers equation with Atangana–Baleanu derivative in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).

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