- Universal Journal of Mathematics and Applications
- Cilt: 7 Sayı: 1
- Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations
Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations
Authors : Dilek Varol, Ayşegül Daşcıoğlu
Pages : 38-45
Doi:10.32323/ujma.1390222
View : 42 | Download : 66
Publication Date : 2024-03-18
Article Type : Research
Abstract :This paper discusses the linear fractional Fredholm-Volterra integro-differential equations (IDEs) considered in the Caputo sense. For this purpose, Laguerre polynomials have been used to construct an approximation method to obtain the solutions of the linear fractional Fredholm-Volterra IDEs. By this approximation method, the IDE has been transformed into a linear algebraic equation system using appropriate collocation points. In addition, a novel and exact matrix expression for the Caputo fractional derivatives of Laguerre polynomials and an associated explicit matrix formulation has been established for the first time in the literature. Furthermore, a comparison between the results of the proposed method and those of methods in the literature has been provided by implementing the method in numerous examples.Keywords : Caputo fractional derivatives, Fredholm-Volterra integro-differential equations, Laguerre polynomials