The fractional differential equations involving different types of fractional derivatives are
currently used in many fields of science and engineering. Therefore, the first purpose of this …

In this article, we develop the natural transform in terms of the M-derivative. We improve the
basic notions for this new interesting version of the fractional transform. We introduce the …

This work aims at a new semi-analytical technique called the Adomian decomposition
method for the analysis of time-fractional Emden–Fowler equations. The Laplace …

In this paper, we consider a tuberculosis model with incomplete treatment and extend the
model to a Caputo fractional-order and two-patch version with exogenous re-infection …

The nonlinear conformable fractional Schrödinger–Hirota (NCFSH) equation, describing the
propagation of optical solitons in a dispersive optical fibre, is considered and its exact …

In this work, two different schemes, the extended hyperbolic auxiliary and the simplest
equation method, are employed to construct the exact solutions involving parameters of the …

The aim of the paper is to find the exact solutions to the nonlinear partial differential
equations of fractional-order. The simplest equation procedure is handled for this purpose …

In this paper, exact analytical solutions of the biological population model, the EW and the
modified EW equations with a conformable derivative operator have been examined by …

The most popular fields of interdisciplinary studies for real-world applications, such as
population growth dynamics, diffusion–reaction, and Duffing models, are concerned with …

This study investigates exact analytical solutions of some nonlinear partial differential
equations arising in mathematical physics. To this reason, the Kudryashov-Sinelshchikov …