A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Sandeep Kumar, Rajesh K. Pandey, H. M. Srivastava and G. N. Singh
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Sandeep Kumar: Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India
Rajesh K. Pandey: Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India
H. M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
G. N. Singh: Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, Jharkhand, India

Mathematics, 2021, vol. 9, issue 9, 1-17

Abstract: In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

Keywords: collocation method; B-operator; Jacobi poly-fractonomials; fractional integro-differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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