Fractional Order Fredholm Integro-Differential Equations: A Numerical Solution Applying Collocation Points
Ganiyu Ajileye
*
Department of Mathematics, Federal University, Wukari, Taraba State, Nigeria.
Richard Taparki
Department of Mathematical Sciences, Taraba State University, Jalingo, Taraba State, Nigeria.
Ojo Olamiposi Aduroja
Department of Mathematics, University of Ilesa, Ilesa, Osun State, Nigeria.
Rahimat Oziohu Onsachi
Department of Mathematical Sciences, Kogi State University, Kabba, Kogi State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Integro-differential equations are applied to model physical phenomena in science and engineering. They are found in many mathematical representations of physical phenomena (IDEs). Kinetic equations describing the kinetic theory of rarefied gases, plasma, coagulation, and radiation transport are a few problems. In this work, we developed and applied a numerical approach to solve Fredholm integro-differential equations of fractional order with collocation points. After obtaining the problem's integral form, we used the collocation points to convert it into an algebraic system of equations. We use matrix inversion to solve the algebraic equation. An analysis of the developed approach revealed that the results were convergent and continuous. Furthermore, it was shown that the answer was unique. The effectiveness and consistency of the technique were assessed using numerical examples.
Keywords: Collocation points, integro-differential equation, fractional derivatives, fredholm, approximate solution