Abstract
The main purpose of this study gears towards finding numerical solution to fractional integro-differential equations. The technique involves the application of caputo properties and Chebyshev polynomials to reduce the problem to system of linear algebraic equations and then solved using MAPLE 18. To demonstrate the accuracy and applicability of the presented method some numerical examples are given. Numerical results show that the method is easy to implement and compares favorably with the exact results. The graphical solution of the method is displayed.
Highlights
Fractional integro-differential equations has played a significant role in modelling of real world physical problems e.g the modeling of earthquake, reducing the spread of virus, control the memory behaviour of electric socket and many others
Numerical solution to Fractional Integro-diffrential Equations (FIDEs) in different fields has been a point of attraction for researchers in recent times. [4] employed Lagurre polynomials as basis functions for the solution of fractional Solving Fredholm integro-differential equations while [5] employed Bernstein polynomials as basis functions to approximate the solution of FIDEs
References [11 - 12] used Least - Squares method for the solution of FIDEs. [13,14,15] introduced numerical solution of fractional singular integro-differential equations by using Taylor series expansion and Galerkin method and a fast numerical algorithm based on the second kind of Chebyshev polynomials
Summary
Fractional integro-differential equations has played a significant role in modelling of real world physical problems e.g the modeling of earthquake, reducing the spread of virus, control the memory behaviour of electric socket and many others. Since most Fractional Integro-diffrential Equations (FIDEs) cannot be solved analytically, approximation and numerical techniques, they are used extensively. [4] employed Lagurre polynomials as basis functions for the solution of fractional Solving Fredholm integro-differential equations while [5] employed Bernstein polynomials as basis functions to approximate the solution of FIDEs. References [6 - 8] applied collocation techniques for solving FIDEs using different basis functions. [9] applied Sumudu transform method and Hermite Spectral collocation method for solving FIDEs. Author [10] introduced approximate solutions of Volterra-Fredholm integro-differential equations of fractional order. The author in [16] applied numerical solution of Fredholm-Volterra fractional integrodifferential equation with nonlocal boundary conditions
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