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

Jagdev Singh, Arpita Gupta and Devendra Kumar ()
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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

Mathematics, 2023, vol. 11, issue 3, 1-17

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.

Keywords: Prabhakar function; Caputo–Prabhakar fractional derivative; fractional Riccati differential equation; numerical method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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