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 : 51 | Download : 73

Publication Date : 2024-03-18

Article Type : Research Paper

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