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A new approach by two‐dimensional wavelets operational matrix method for solving variable‐order fractional partial integro‐differential equations
Author(s) -
Saha Ray Santanu
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22530
Subject(s) - mathematics , algebraic equation , variable (mathematics) , wavelet , fractional calculus , legendre wavelet , partial differential equation , convergence (economics) , partial derivative , matrix (chemical analysis) , order (exchange) , collocation method , collocation (remote sensing) , legendre polynomials , differential equation , mathematical analysis , wavelet transform , computer science , discrete wavelet transform , ordinary differential equation , nonlinear system , materials science , artificial intelligence , economic growth , composite material , quantum mechanics , physics , finance , economics , machine learning
In this paper, a new computational scheme based on operational matrices (OMs) of two‐dimensional wavelets is proposed for the solution of variable‐order (VO) fractional partial integro‐differential equations (PIDEs). To accomplish this method, first OMs of integration and VO fractional derivative (FD) have been derived using two‐dimensional Legendre wavelets. By implementing two‐dimensional wavelets approximations and the OMs of integration and variable‐order fractional derivative (VO‐FD) along with collocation points, the VO fractional partial PIDEs are reduced into the system of algebraic equations. In addition to this, some useful theorems are discussed to establish the convergence analysis and error estimate of the proposed numerical technique. Furthermore, computational efficiency and applicability are examined through some illustrative examples.