# Collocation Approach for the Computational Solution Of Fredholm-Volterra Fractional Order of Integro-Differential Equations

## Authors

• Ganiyu Ajileye Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
• Adewale James Department of Mathematics, American University of Nigeria, Yola, Adamawa State, Nigeria.
• Ayinde Abdullahi Department of Mathematics, Moddibo-Adama University, Yola Nigeria.
• Taiye Oyedepo Federal College of Dental Technology and Therapy, Enugu, Nigeria.

## Keywords:

FREDHOLM-VOLTERRA, Collocation, Integro-differential

## Abstract

In this work, a collocation technique is used to determine the computational solution to fractional order Fredholm-Volterra integro-differential equations with boundary conditions using Caputo sense. We obtained the linear integral form of the problem and transformed it into a system of linear algebraic equations using standard collocation points. The matrix inversion approach is adopted to solve the algebraic equation and substituted it into the approximate solution. We established the uniqueness and convergence of the method and some modelled numerical examples are provided to demonstrate the method’s correctness and efficiency. It is observed that the results obtained by our new method are accurate and performed better than the results obtained in the literature. The study will be useful to engineers and scientists. It is advantageous because it addresses the difficulty in tackling fractional order Fredholm-Volterra integro-differential problems using a simple collocation strategy. The approach has the advantage of being more accurate and reducing computer running time.

Dimensions

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2022-10-03

## How to Cite

Ajileye, G. ., James, A., Abdullahi, A. ., & Oyedepo, T. (2022). Collocation Approach for the Computational Solution Of Fredholm-Volterra Fractional Order of Integro-Differential Equations. Journal of the Nigerian Society of Physical Sciences, 4(4), 834. https://doi.org/10.46481/jnsps.2022.834

## Section

Original Research