Numerical comparisons for solving fractional order integro-differential equations with non-local boundary conditions

Abstract

In this paper, univariate Pade approximation is applied to fractional power sries solutions of fractional integro-differential equations with non-local boundary conditions. As it is seen from comparisons, univariate Pade approximation gives reliable solutions and numerical results.

Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial

“…The same problem was solved in [25] and obtained approximate solution using Pade approximations with maximum absolute error of 8.69×10 −5 , likewise [10] used Bernstein polynomials as an approximating polynomial and obtained 4.90 × 10 −11 as maximum absolute error at N = 4 while in the proposed scheme, we obtain exact solution at N = 1. The same problem was solved in Ref.…”

“…Convergence of Jacobi spectral collocation method was investigated in the solution of FIE by Huang et al [17,18], FIE with weakly singular kernel was studied using legendre wavelets method by Yi et al [19], spline collocation method was used to solve fractional weakly singular IDEs by Pedas et al [20]. Two-dimensional non-linear Volterra-Fredholm IDEs was investigated using variational ADM by Hendi & Al-Qarni [21], He et al [22,23] studied a system of linear Fredholm integral equations using Bernstein and improved Block-Pulse functions, collocation method couple with convergence was employed to solve generalized FIE by Sharma et al [24], Turut [25] adopted pade approximation technique to solve FIE with non-local boundary conditions, modified Laplace decomposition method was developed to solve fractional Volterra-Fredholm IDEs by Hamoud & Ghadle [26], Gupta & Pandey [27] proposed adaptive huber method for weakly singular fractional integro-differential equations, analysis of the error involved in 1D Fredholm integro-differential equations was studied by Fairbairn & Kelmanson [28] using Volterra-transformation method, Wang et al [29] proposed a method based on Laplace transform for finding an approximate solution to Fredholm-type integro-differential equation with Atangana-Baleanu fractional derivative in Caputo sense, Toma & Postavaru [30] transformed IDEs to algebraic form using Newton's iterative method then investigate the accuracy of the proposed method.…”