In this paper, a tutorial introduction to the two-scale fractal calculus is given. The two-scale
fractal derivative is conformable with the traditional differential derivatives. When the fractal …

Fractional differential equations depict nature sufficiently in light of the symmetry properties
which describe biological and physical processes. This article is concerned with the …

The comprehensive formularization of the frequency–amplitude formula is the main interest
in this work to cover higher powers of the restoring force which are not limited to cubic …

In this article, we construct exact solutions of the Bogoyavlenskii equation using (1/G′)-
expansion and (G′/G, 1/G)-expansion techniques. Both techniques have been successfully …

This manuscript focuses on the application of the (m+ 1/G′)-expansion method to the (2+ 1)-
dimensional hyperbolic nonlinear Schrödinger equation. With the help of projected method …

Numerous scientific fields depend on precise solutions, which can be obtained for nonlinear
partial differential equations (PDEs) through various techniques. It is important to note that …

In this article, the soliton solutions of the Gilson–Pickering equation have been constructed
using the sinh-Gordon function method (ShGFM) and (G′/G, 1/G)-expansion method, which …

In this article, a simple and new algorithm is proposed, namely the modified variational
iteration algorithm-I (mVIA-I), for obtaining numerical solutions to different types of fifth-order …

In this work, it is used three families of nonlinearities such as Kerr law, Power Law and
Parabolic law over the High-order dispersive Nonlinear Schrödinger equation to inquire …

This study aims to investigate the (2+ 1)-dimensional Kadomtsev-Petviashvili equation via
the three-waves method through the Hirota bilinear form and the Kudryashov's method. Multi …