An operational matrix of fractional integration of the Laguerre polynomials and its application on a semi-infinite interval

Abstract

In this study, we consider a linear nonhomogeneous differential equation with variable coefficients and variable delays and present a novel matrix-collocation method based on Morgan-Voyce polynomials to obtain the approximate solutions under the initial conditions. The method reduces the equation with variable delays to a matrix equation with unknown MorganVoyce coefficients. Thereby, the solution is obtained in terms of Morgan-Voyce polynomials. In addition, two test problems together with error analysis are performed to illustrate the accuracy and applicability of the method; the obtained results are scrutinized and interpreted by means of tables and figures.

Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream

“…As it is known, the spectral method is one of the flexible methods of discretization for most types of differential equations [38][39][40]. Historically, spectral method has been relegated to fractional calculus, but in few years, it has been successfully applied for the fractional equation models based on the different types of orthogonal polynomials such as Block pulse functions [41,42], Legendre polynomials [43][44][45][46], Chebyshev polynomials [47][48][49], Laguerre polynomials [50][51][52][53], and Bernstein polynomials [54][55][56]. Doha et al [57] introduced the shifted Jacobi operational matrix of fractional derivative which is based on Jacobi tau method for solving numerically linear multiterm fractional differential equations with initial or boundary conditions.…”

“…Hence, the variational formulation of (56) according to Relation (14) in [65], by means of a typical tau method like in the crisp context [29] and (52), is equivalent to…”

“…be the fuzzy exact solution of (49), and ( ) is the best fuzzy Jacobi approximate function (52), and suppose that…”

Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

“…The method based on the orthogonal functions is a wonderful and powerful tool for solving the FDEs and has enjoyed many successes in this realm. The operational matrix of fractional integration has been determined for some types of orthogonal polynomials, such as Chebyshev polynomials [16], Legendre polynomials [22], Laguerre polynomials [23][24][25], and Jacobi polynomials [26]. Moreover, the operational matrix of fractional derivative for Chebyshev polynomials [9] and Legendre polynomials [9,14] also has been derived.…”

Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

“…Since most FDEs do not have exact analytic solutions, many researchers have tried to find solutions of FDEs using approximate and numerical techniques. For example see [3,12,16,[20][21][22][23][24]. Our aim in this work is the following type of multi-order FDE:…”