In this paper, we study fractional‐order optimal control problems (FOCPs) involving the
Atangana‐Baleanu fractional derivative. A computational method based on B‐spline …

This paper aims to provide a rigorous analysis of exponential convergence of an adaptive
spectral collocation method for a general nonlinear system of rational-order fractional initial …

We introduce a class of orthogonal functions associated with integral and fractional
differential equations with a logarithmic kernel. These functions are generated by applying a …

In this paper, we consider a new fractional function based on Legendre and Laguerre
polynomials for solving a class of linear and nonlinear time-space fractional partial …

Many PDEs involving fractional Laplacian are naturally set in unbounded domains with
underlying solutions decaying slowly and subject to certain power law. Their numerical …

A family of orthogonal systems of fractional functions is introduced. The proposed orthogonal
systems are based on Jacobi polynomials through a fractional coordinate transform. This …

In this article, a new numerical scheme space Spectral time Fractional Adam Bashforth
Moulton method for the solution of fractional partial differential equations is offered. The …

This paper provides the Riesz potential and fractional Laplacian (− Δ) s, s∈ R of the famous
radial kernels, including the Gaussian, multiquadric, Sobolev spline, and mainly focuses on …

This work is concerned with spectral collocation methods for fractional PDEs in unbounded
domains. The method consists of expanding the solution with proper global basis functions …

In this paper, we have developed the spectral theory for a conformable fractional Sturm-
Liouville problem L α (q (x), h, H) with boundary conditions which include conformable …