Abstract
We employ the Polynomial Least Squares Method as a relatively new and very straightforward and efficient method to find accurate approximate analytical solutions for a class of systems of fractional nonlinear integro-differential equations. A comparison with previous results by means of an extensive list of test-problems illustrate the simplicity and the accuracy of the method.
Highlights
The notion of a fractional derivative as a derivative of any arbitrary real or complex order has a long history, starting with the works of early titans of mathematics such as Leibniz, Abel, Liouville and Heaviside
Least Squares Method, in Section 3, we present the results of an extensive testing process involving most of the usual test problems included in similar studies and in Section 4 we present the conclusions of the study
The simplicity of the method—the computations involved in the use of PLSM are as straightforward as it gets; in the case of a lower degree polynomial the computations sometimes can be performed even by hand, as illustrated by the first application
Summary
The notion of a fractional derivative as a derivative of any arbitrary real or complex order has a long history, starting with the works of early titans of mathematics such as Leibniz, Abel, Liouville and Heaviside. Chebyshev wavelets as a basis and transforms the problem into a system of algebraic equations These methods usually yield solutions with very low errors which converge relatively fast. In 2015, Khalil and Khan used the Shifted Legendre Polynomials Method [12] to solve a coupled system of linear Fredholm integro-differential equations In this method the initial problem is transformed into a series of algebraic equations of the shifted. The method transforms the problem into a system of algebraic equations by means of a Bernoulli wavelets basis expansion and the examples show relatively low errors and illustrate the convergence. In 2021, Duangpan et al used the Finite Integration Method [22] to find approximate solutions for systems of linear fractional Volterra integro-equations by transforming them in systems of algebraic equations via Shifted Chebyshev Polynomials. Least Squares Method (denoted from this point forward as PLSM), in Section 3, we present the results of an extensive testing process involving most of the usual test problems included in similar studies and in Section 4 we present the conclusions of the study
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