Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory
Jagdev Singh, Arpita Gupta, Devendra Kumar
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.
Topics & Concepts
MathematicsRiccati equationUniquenessNonlinear systemConvergence (economics)Fractional calculusScheme (mathematics)Reliability (semiconductor)Applied mathematicsAlgebraic Riccati equationDifferential equationMathematical analysisQuantum mechanicsPhysicsEconomic growthEconomicsPower (physics)Fractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNonlinear Waves and Solitons