Computational Algorithm for Fractional Fredholm Integro-Differential Equations

Abstract

Fractional calculus is a fascinating field of mathematics that focuses on the study of integrals and derivatives of arbitrary orders, extending the principles of basic calculus. Its applications span across various scientific, engineering, and other disciplines. In this study, the collocation method, in conjunction with the utilization of the fourth kind Chebyshev polynomials, is employed to explore solutions for fractional integro-differential equations of Fredholm type. By applying the collocation method, the problem at hand is transformed into a system of linear algebraic equations. These equations are subsequently solved by employing matrix inversion techniques to determine the unknown constants. To provide a comprehensive understanding and visualization of the results, the research incorporates tables and figures, which present numerical examples and comparisons. These comparisons serve to highlight the superior performance of the proposed method in terms of efficiency and convenience when compared to traditional methods. By showcasing the advantages of the collocation method and the utilization of fourth kind Chebyshev polynomials, the research underscores the potential of these approaches in solving fractional integro-differential equations.