Numerical Computations of Fractional Differential Equations in Engineering using the Polynomial Least Squares Method
Keywords:
Caputo Fractional Derivative; Fractional Calculus; Numerical Analysis; Fractional Differential Equations; Polynomial Least Squares Method.Abstract
Fractional differential equations appear in the modeling of science and engineering phenomena including classical mechanics, quantum mechanics, thermodynamics, fluid mechanics, relativity theory and chemical engineering. In this paper, the least squares method is used to find the numerical solution of fractional differential equations appearing in mechanics and engineering. The increasing interest in applications of fractional calculus has motivated the development and study of numerical methods specifically created to solve fractional differential equations. A unique feature is that engineers, physicists and scientists come across processes which lead to involve fractional differential equations. When dealing with more complicated systems with no precise solutions other than approximations, numerical methods are relied on to obtain solutions. The suggested method is used to solve various linear and non-linear problems of constant-order. The proposed scheme is found to be computationally effective with fast convergence.
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