NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH INITIAL CONDITIONS USING COLLOCATION APPROACH
AJILEYE, G., Aduroja, O., Ajileye, A., OYEDEPO, T. (2025). NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH INITIAL CONDITIONS USING COLLOCATION APPROACH. EKB Journal Management System, 16(1), 1-10. doi: 10.21608/jfca.2024.290528.1101
GANIYU AJILEYE; Ojo O Aduroja; Adewole Mukaila Ajileye; TAIYE OYEDEPO. "NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH INITIAL CONDITIONS USING COLLOCATION APPROACH". EKB Journal Management System, 16, 1, 2025, 1-10. doi: 10.21608/jfca.2024.290528.1101
AJILEYE, G., Aduroja, O., Ajileye, A., OYEDEPO, T. (2025). 'NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH INITIAL CONDITIONS USING COLLOCATION APPROACH', EKB Journal Management System, 16(1), pp. 1-10. doi: 10.21608/jfca.2024.290528.1101
AJILEYE, G., Aduroja, O., Ajileye, A., OYEDEPO, T. NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH INITIAL CONDITIONS USING COLLOCATION APPROACH. EKB Journal Management System, 2025; 16(1): 1-10. doi: 10.21608/jfca.2024.290528.1101

NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH INITIAL CONDITIONS USING COLLOCATION APPROACH

Journal of Fractional Calculus and Applications
Volume 16, Issue 1, 2025, Page 1-10  XML PDF (343.23 K)
Document Type: Regular research papers
DOI: 10.21608/jfca.2024.290528.1101
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Authors
GANIYU AJILEYE email 1; Ojo O Aduroja2; Adewole Mukaila Ajileye3; TAIYE OYEDEPO4
1Department of Mathematics and Statistics, Federal University Wukari, Taraba State
2Department of Mathematics, University of Ilesa, Ilesa, Osun State, Nigeria.
3Department of Mathematics, University of Ilesa, Ilesa, Osun State, Nigeria
4Federal College of Dental Technology and Therapy, Enugu, Nigeria
Abstract
In this paper, we develop and implement a numerical method for the solution of Volterra integro- differential equations of fractional order using the collocation method. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the polynomial collocation method. We then solve the algebraic equation using matrix inversion. The analysis of the developed method was investigated, and the solution was found to be continuous, and convergent. The uniqueness of the solution was also proven. Numerical examples were considered to test the consistency and efficiency of the method.
In this paper, we develop and implement a numerical method for the solution of Volterra integro- differential equations of fractional order using the collocation method. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the polynomial collocation method. We then solve the algebraic equation using matrix inversion. The analysis of the developed method was investigated, and the solution was found to be continuous, and convergent. The uniqueness of the solution was also proven. Numerical examples were considered to test the consistency and efficiency of the method.
Keywords
Standard collocation; Volterra; Integro-differential; Fractional; Caputo derivative
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