Homotopy Analysis Fractional Sumudu Transform Method for Semi-analytic Solution of 2-D Time-Fractional Black–Scholes Equations

Authors

Rishi Kumar Pandey, Symbiosis Centre for Management Studies (SCMS), Symbiosis International (Deemed University)(SIU), Mouza-Wathoda, Nagpur, Maharastra, IndiaFollow
Ram Kishun Lodhi, Department of Applied Science, Symbiosis Institute of Technology, Symbiosis International (Deemed University) Pune-412115, (Maharashtra), IndiaFollow
Kottakkaran Sooppy Nisar, Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi ArabiaFollow
Osama Moaaz, Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaFollow
Hegagi M. Ali, Department of Mathematics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi ArabiaFollow

Abstract

Through two assets of the European call option into the form of a time-fractional order Caputo derivative, we have addressed the time-fractional Black-Scholes equations in the current paper. The homotopy analysis fractional Sumudu transform technique has been used to acquire the analytical solution through the convergence of the series solution. The approach combines the Sumudu transform and homotopy analysis approaches. Several graphs at specific and varying parameter values display the solution analysis and variations.

Recommended Citation

Kumar Pandey, Rishi; Kishun Lodhi, Ram; Sooppy Nisar, Kottakkaran; Moaaz, Osama; and M. Ali, Hegagi (2023) "Homotopy Analysis Fractional Sumudu Transform Method for Semi-analytic Solution of 2-D Time-Fractional Black–Scholes Equations," Information Sciences Letters: Vol. 12 : Iss. 11 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol12/iss11/11