# A numerical method for solving non-linear volterra integro-differential equation of fractional order

Document Type : Original Article

Authors

1 Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria

2 Department of mathematics, University of Ilesa, Ilesa, Osun State. Nigeria

3 Department of Mathematics, University of Abuja, Abuja, Nigeria

Abstract

In this paper, we develop and implement numerical method for the solution of non-linear Volterra integro-differential equations of fractional order using collocation method. We obtain the integral form of the problem and transform it into system of algebraic equations, we solve the algebraic equations using matrix inversion method. The analysis of the developed method is investigated and solution found to be q-contraction and convergent. The uniqueness of the solution also proven. Numerical examples were considered to test the efficiency of the method which shows that the method compete favourably with the existing methods.

Keywords

Main Subjects

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### History

• Receive Date: 08 June 2023
• Revise Date: 10 December 2023
• Accept Date: 22 December 2023