In this paper, we introduce a new scheme based on the exponential spline function for
solving linear second-order Fredholm integro-differential equations. Our approach consists …

In this paper, we shall solve a time-fractional nonlinear Schrödinger equation by using the
quintic non-polynomial spline and the L 1 formula. The unconditional stability, unique …

In the present article, an efficient operational matrix based on the famous Laguerre
polynomials is applied for the numerical solution of two-dimensional non-linear time …

This paper presents a groundbreaking numerical technique for solving nonlinear time
fractional differential equations, combining the conformable continuity equation (CCE) with …

In this paper, we propose two new approximation methods on a general mesh for the
generalized Caputo fractional derivative of order α∈(0, 1). The accuracy of these two …

In a recent study, we investigate the Burgers–Fisher equation through a developed scheme,
namely, the non-polynomial spline fractional continuity method. The proposed models …

In this paper, we develop a higher order numerical method for the fractional Bagley‐Torvik
equation. The main tools used include a new fourth‐order approximation for the fractional …

In this paper, we develop a new approximation for the generalized fractional derivative,
which is characterized by a scale function and a weight function. The new approximation is …

Using a new generalized L 2 formula and a time varying compact finite difference operator,
we construct a high order numerical scheme for a class of generalized fractional diffusion …

In this article, we develop a higher order approximation for the generalized fractional
derivative that includes a scale function z (t) and a weight function w (t). This is then used to …