Numerical approach for solving fractional Fredholm integro-differential equation

Generalized Spline Method for Integro-Differential Equations of Fractional Order

“…Where q j , j=1,2,…,2n be the basis function of generalized spline S(x),2n is order of L * Lx=0 and c 1 ,c 2 ,…,c 2n are constants to be found. Substituting (3) in (1) we obtain : 3.983 10 -3 -3.983 10 -3 0 1 Figure-1, give the exact solution u(x) and its approximation S(x) for the considered example with the initial conditions ( ) ( ) …(15) the exact solution is, [8]:…”

Iterative refinement for a system of linear integro-differential equations of fractional type

“…One of the most popular methods which attracted the attention of many mathematicians is the Adomian decomposition method [1,2]. Among the other methods are the differential transform method [3], Taylor expansion methods [4,5], spectral methods [6], as well as the variational iteration and homotopy perturbation methods [7,8] -only to name a few. The widespread of these methods enabled the subject of fractional calculus to become a well established discipline in applied mathematics, and thus finding its way into the toolbox of many commercial packages like MATLAB and MATHEMATICA.…”

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).…”