Numerical solutions for the reaction–diffusion, diffusion‐wave, and Cattaneo equations using a new operational matrix for the Caputo–Fabrizio derivative
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DOI: 10.1002/mma.6517
Abstract: In this research work, we study the model of nonlinear reaction–diffusion equation, diffusion‐wave equation, and Cattaneo equation with the help of a numerical method in which time‐fractional derivative is of Caputo–Fabrizio type (C‐F). First, we… read more here.
Keywords: operational matrix; diffusion; equation; diffusion wave ... See more keywords
Müntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations
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DOI: 10.1007/s11075-017-0363-4
Abstract: This paper presents a new computational technique for solving fractional pantograph differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use Müntz-Legendre wavelet and its operational matrix of… read more here.
Keywords: fractional order; order integration; ntz legendre; operational matrix ... See more keywords
An Efficient Operational Matrix Method for a Few Nonlinear Differential Equations Using Wavelets
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DOI: 10.1007/s40819-019-0723-y
Abstract: In this paper, a theoretical model of biofiltration of mixture of hydrophilic (methanol) and hydrophobic (α-pinene) volatile organic compounds is discussed. An efficient wavelet-based operational matrix method is developed for the analytical expressions pertaining to… read more here.
Keywords: efficient operational; method nonlinear; method; matrix method ... See more keywords
Operational matrix based on Genocchi polynomials for solution of delay differential equations
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DOI: 10.1016/j.asej.2016.09.015
Abstract: Abstract In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equations, delay differential equations with neutral terms and delay differential system with constant and variable coefficients.The new method is… read more here.
Keywords: matrix based; genocchi polynomials; differential equations; based genocchi ... See more keywords
B-spline operational matrix of fractional integration
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DOI: 10.1016/j.ijleo.2016.10.066
Abstract: Abstract In this paper, we use the second and third order spline functions to derive the operational matrix of fractional integration, which we then apply to solve fractional integro-differential equations, Abel equations and partial fractional… read more here.
Keywords: fractional integration; operational matrix; spline operational; matrix fractional ... See more keywords
Spectral Solutions of Even-Order BVPs Based on New Operational Matrix of Derivatives of Generalized Jacobi Polynomials
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DOI: 10.3390/sym15020345
Abstract: The primary focus of this article is on applying specific generalized Jacobi polynomials (GJPs) as basis functions to obtain the solution of linear and non-linear even-order two-point BVPs. These GJPs are orthogonal polynomials that are… read more here.
Keywords: generalized jacobi; jacobi polynomials; even order; operational matrix ... See more keywords