Ten non-polynomial cubic splines for some classes of Fredholm integral equations

On the numerical solution of Volterra and Fredholm integral equations using the fractional spline function method

“…To get a unique solution for ( 5) and ( 6), we get the following equations by using fractional Taylor series. (7) F SM 1…”

“…Currently, many researchers used fractional calculus to derive problems in mathematical science, computer science, physical science and engineering, see [7], [12], [9] and [13], the fractional operator has many definitions, including the Riemann's, Liouville's, Gruwald-Letnikov's, Riemann-Liouville's, and Caputo's fractional integrals and derivatives.…”

“…Recently, some works have been done on this model type, but with natural orders, see [1], [7], [14], [10], [8], [4], and [15], so that is why the proposed technique will be the beginning of a more detailed work on fractional models and perhaps it can progress the topic. This work is organized as follows: the researchers proposed two new types of fractional Spline method (FSM) to solve Volterra and Fredholm-integral equations by using two systems of equations as shown in Section 2 and Section 3, in Section 4 the convergence of these two fractional Spline models have been investigated, in Section 5 numerical examples are presented to illustrate the applications and effectiveness of the approach.…”

Non-polynomial fractional spline method for solving Fredholm integral equations

“…Integral equations can be used to describe some difficulties as well Bellour, A. [5] solving Fredholm integral equations by using two cubic spline methods, in [10] D. Hammad, a new general form of Ten non-polynomial cubic splines for some classes of Fredholm integral equations are presented, Maleknejad, Khosrow, Jalil Rashidinia, and Hamed Jalilian in [22], solved Fredholm integral equation via Quintic Spline functions and in [27] S. Saha Ray, and P. K. Sahu. proposed Numerical methods for solving Fredholm integral equations of the second kind.…”

Построение Обобщенных Итерационных Методов, Используемых Для Решения Интегрального Уравнения Фредгольма

“…A great number of works is devoted to the search for the best possible numerical solution of the equation ( 1) by inventing new methods or by granulating and improving previously known methods. Let us mention here only a few of them:wavelet methods [2], Galerkin [10,11], collocation [12,13,14], quadrature [12], Chebyshev and Legendre collocation method [15], Rayleigh-Ritz method [16], deep learning [17], Ten-non polynomial cubic splines method [18], Gaussian process regression [19] and Taylor expansion [20].…”