An approximation method for fractional integro-differential equations

Abstract

Abstract:In this work, an approximation method is proposed for fractional order linear Fredholm type integrodifferential equations with boundary conditions. The Sinc collocation method is applied to the examples and its efficiency and strength is also discussed by some special examples. The results of the proposed method are compared to the available analytic solutions.

Bernoulli polynomials collocation for weakly singular Volterra integro-differential equations of fractional order

“…To determine the solution of (1) under condition (2), replacing the row vector (14) by the first row of (13), the following new augmented matrix is established…”

Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials

“…Since the fractional calculus has attracted much more interest among mathematicians and other scientists, the solutions of the fractional integrodifferential equations have been studied frequently in recent years (Alkan & Hatipoglu 2017;Hamoud & Ghadle 2018a, 2018bIbrahim et al 2015;Kumar et al 2017;Ma & Huang 2014;Nemati et al 2016;Ordokhani & Dehestani 2016;Parand & Nikarya 2014;Pedas et al 2016;Shahooth et al 2016;Turmetov & Abdullaev 2017;Wang & Zhu 2016;Yi et al 2016). The methods that are used to find the solutions of the linear fractional Fredholm integro-differential equations are given as fractional pseudospectral integration matrices (Tang & Xu 2016), least squares with shifted Chebyshev polynomials Mohammed 2014), least squares method using Bernstein polynomials (Oyedepo et al 2016), fractional residual power series method (Syam 2017), Taylor matrix method (Gülsu et al 2013), reproducing kernel Hilbert space method (Bushnaq et al 2016), second kind Chebyshev wavelet method (Setia et al 2014), open Newton method (Al-Jamal & Rawashdeh 2009), modified Homotopy perturbation method (Elbeleze et al 2016), Sinc collocation method (Emiroglu 2015).…”