A new class of operational matrices method for solving fractional neutral pantograph differential equations

Abstract

This paper uses new fractional integration operational matrices to solve a class of fractional neutral pantograph delay differential equations. A fractional-order function space is constructed where the exact solution lies in, and a set of orthogonal bases are given. Using them, we reduce the fractional delay differential equation to algebraic equations and get the approximate solution. Finally, we give the Legendre operational matrix of fractional integration to solve the equation as an example and show the efficiency of the method.

Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations

“…The generalized Laguerre polynomials in Bhrawy et al 27 and the Genocchi polynomials in Isah et al 26 are used for solving fractional pantograph equations with variable coefficients. In Shi et al, 28 the Legendre polynomials have been utilized to solve fractional panto-graph equations. The fractional Bernoulli wavelets, 29 the Taylor wavelets, 30 and the fractional Taylor wavelets 31 as some of well-known wavelets have been recently used for solving fractional pantograph equations.…”

A New Algorithm Based on Bernstein Polynomials Multiwavelets for the Solution of Differential Equations Governing AC Circuits

“…AC circuits include features that are used in a variety of everyday gadgets. Many numerical methods based on different operational matrices have been developed to determine solutions of differential equations with a given degree of accuracy [1][2][3][4] Wavelets were also used for solving several physical problems [5][6][7][8]. In this paper, we show the application of the proposed method in LCR (electric circuit comprising of resistance (R), capacitor (C) and inductor (L)) and L-C circuits (comprising of inductor (L) and capacitor (C)) circuits see Figure 1.…”