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.
Highlights
Fractional calculus is a generalization of calculus to an arbitrary order
This paper is devoted to obtaining a class of operational matrices based on different type of fractional orthogonal polynomials and solving the fractional neutral pantograph delay differential equations by the obtained operational matrices
We give the appropriate space where we find the approximate solution of fractional differential equations
Summary
Fractional calculus is a generalization of calculus to an arbitrary order. In recent years, it is extensively applied to various fields such as viscous elastic mechanics, power fractal networks, electronic circuits [1,2,3]. With the help of these matrices and orthogonal polynomials, we can reduce a fractional differential or integral equation to algebraic equations, and get the approximate solution. Much research in this field has emerged, such as Legendre operational matrices [1,2,3], Chebyshev operational matrices [4], block pulse operational matrices [5]. This paper is devoted to obtaining a class of operational matrices based on different type of fractional orthogonal polynomials and solving the fractional neutral pantograph delay differential equations by the obtained operational matrices. We construct suitable fractional orthogonal polynomials and get the better operational matrices based on the order of the fractional differential or integral equation. Proof Let Kmα be the operational matrix of fractional integration for Um(x).
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