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Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory

Author

Listed:
  • Jagdev Singh

    (Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India)

  • Arpita Gupta

    (Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India)

  • Devendra Kumar

    (Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India)

Abstract

The key objective of the current work is to examine the behavior of the nonlinear fractional Riccati differential equation associated with the Caputo–Prabhakar derivative. An efficient computational scheme, that is, a mixture of homotopy analysis technique and sumudu transform, is used to solve the nonlinear fractional Riccati differential equation. The convergence and uniqueness analysis for the solution of the implemented technique is shown. In addition, the numerical consequences are demonstrated in the form of graphical representations to verify the reliability of the applied method in obtaining the solution to the mathematical model with Prabhakar-type memory.

Suggested Citation

  • Jagdev Singh & Arpita Gupta & Devendra Kumar, 2023. "Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory," Mathematics, MDPI, vol. 11(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:644-:d:1048161
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    References listed on IDEAS

    as
    1. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    2. Xin Liu & Kamran & Yukun Yao & Ljubisa Kocinac, 2020. "Numerical Approximation of Riccati Fractional Differential Equation in the Sense of Caputo-Type Fractional Derivative," Journal of Mathematics, Hindawi, vol. 2020, pages 1-12, September.
    3. Mehmet Merdan, 2012. "On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-17, May.
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