This paper presents an investigation of soliton solutions for the perturbed Fokas-Lenells
(pFL) equation, which has a vital role in optics, using Sardar sub-equation method. The …

In the present case, we propose the correct version of the fractional Adams-Bashforth
methods which take into account the nonlinearity of the kernels including the power law for …

Mathematical analysis with the numerical simulation of the newly formulated fractional
version of the Adams-Bashforth method using the Atangana-Baleanu operator which has …

In this work, the solution of Riesz space fractional partial differential equations of parabolic
type is considered. Since fractional-in-space operators have been applied to model …

Variable-order differential operators can be employed as a powerful tool to modeling
nonlinear fractional differential equations and chaotical systems. In this paper, we propose a …

In this paper, a robust numerical simulation technique based on the fractional Adams–
Bashforth and the Fourier spectral methods are formulated to explore some spatiotemporal …

Many chemical systems exhibit a range of patterns, a noticeable and interesting class of
numerical patterns that arise in autocatalytic reactions which changes with increasing spatial …

Recently a new fractional differentiation was introduced to get rid of the singularity in the
Riemann-Liouville and Caputo fractional derivative. The new fractional derivative has then …

An epidemic system of HIV/AIDS transmission is examined in this paper. The classical time
derivative is modelled with the Atangana-Baleanu nonlocal and nonsingular fractional …

In this paper, the malaria transmission (MT) model under control strategies is considered
using the Liouville–Caputo fractional order (FO) derivatives with exponential decay law and …