Numerical solution of variable‐order stochastic fractional integro‐differential equation with a collocation method based on Müntz–Legendre polynomial. (20th January 2022)

• Record Type: Journal Article
• Authors: Kumar Singh, Abhishek; Mehra, Mani; Mehandiratta, Vaibhav
• Other Names: Nizovtseva Irina guestEditor.; Alexandrov Dmitri guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 13(2022)
• Page Start: 8125
• Page End: 8141
• Publication Date: 2022-01-20
• Subjects: integro‐differential equations -- Müntz–Legendre polynomial -- operational matrix -- variable‐order fractional differential equations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8076
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this work, our motivation is to design a new collocation method based on Müntz–Legendre polynomial involving operational matrices to solve variable‐order stochastic fractional integro‐differential equation. We first prove the existence and uniqueness result for the solution of considered problem. The operational matrices are used to convert the variable‐order stochastic fractional integro‐differential equation into non‐linear system of algebraic equations. Further, the accuracy and efficiency of the proposed method are investigated through numerical experiments. Finally, we show the advantage of the variable‐order model over the constant order model through a real‐world example of mathematical finance.