In this study, we introduce a nonlinear leukemia dynamical system for a piecewise modified
ABC fractional-order derivative and analyze it for the theoretical as well computational works …

Different types of fractional derivatives have recently been noticed by researchers and used
in modeling phenomena due to their characteristics. Furthermore, fractional optimal control …

In this article, an analytical technique based on unified method is applied to investigate the
exact solutions of non-linear homogeneous evolution partial differential equations. These …

In comparison to fractional-order differential equations, integer-order differential equations
generally fail to properly explain a variety of phenomena in numerous branches of science …

Fractional diffusion partial differential equation (PDE) models are used to describe
anomalous transport phenomena in fractal porous media, where traditional diffusion models …

The longitudinal vibrationnal analysis of an irregular single-walled carbon nanotube
(ISWCNT) with elastic boundary restraints along its ends is invistigated in this study. The …

This paper analyzes a novel use of the shifted Fibonacci polynomials (SFPs) to treat the
timefractional Burgers equation (TFBE). We first develop the fundamental formulas of these …

This manuscript presents enhanced versions of two methods: the natural transform iterative
method (NTIM) and the q-homotopy analysis method (q-HAM). These methods harness …

In this study, we provide an efficient simulation to investigate the behavior of the solution to
the Brusselator system (a biodynamic system) with the Rabotnov fractional-exponential …

In this study, we consider a new class of nonlinear integro-differential equations with the
Bessel fractional integral-derivative. For solving the considered equations, fractional-order …