General Lagrange scaling functions: application in general model of variable order fractional partial differential equations

چکیده مقاله

This paper studies a numerical technique to solve general variable-order partial differential equations. We present a general variable-order Riemann-Liouville pseudo-operational matrix and a general variable-order fractional derivative pseudo-operational matrix for the general Lagrange scaling functions (GLSFs). These matrices are achieved generally, without considering the nodes of Lagrange polynomials. Next, by implementing the obtained pseudo-operational matrices and an optimization method, the considered problem reduces to a system of nonlinear algebraic equations. Additionally, the convergence analysis is proposed and three numerical examples illustrate its good performance. © 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.