Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader
area of fractional calculus that has important and far-reaching applications for the modeling …

Recently, operational matrices were adapted for solving several kinds of fractional
differential equations (FDEs). The use of numerical techniques in conjunction with …

Herein, we adduce, analyze, and come up with spectral collocation procedures to iron out a
specific class of nonlinear singular Lane–Emden (LE) equations with generalized Caputo …

This paper presents the nonlinear systems of Volterra‐type fractional integro‐differential
equation solutions through a Chebyshev pseudospectral method. The proposed method is …

This paper obtains soliton solutions to optical couplers by two methods. These are sine–
cosine function method and Bernoulli's equation approach. There are four laws that are …

This paper applied the trial solution technique to chiral nonlinear Schrodinger's equation in
(1++ 2)-dimensions. This led to solitons and other solutions to the model. Besides soliton …

Current discretizations of variable-order fractional (V-OF) differential equations lead to
numerical solutions of low order of accuracy. This paper explores a high order numerical …

In a fractional optimal control problem, the integer order derivative is replaced by a fractional
order derivative. The fractional derivative embeds implicitly the time delays in an optimal …

A shifted Legendre collocation method in two consecutive steps is developed and analyzed
to numerically solve one-and two-dimensional time fractional Schrödinger equations …

In this study, the intelligent computational strength of neural networks (NNs) based on the
backpropagated Levenberg‐Marquardt (BLM) algorithm is utilized to investigate the …