In this work, a new adaptive numerical method is proposed for solving nonlinear, singular,
and stiff initial value problems often encountered in real life. Starting with a fixed step size …

In this study, the nonlinear perturbed Schrödinger equation (NPSE) with nonlinear terms as
quadratic-cubic law nonlinearity media with the beta derivative is investigated and this …

The space–time fractional Gardner and Zakharov–Kuznetsov–Benjamin–Bona–Mahony
(ZKBBM) equations are used to explain the transmission of shallow water waves inside a …

In this paper, the bidirectional wave model is described by using the local fractional
derivative (LFD) on Cantor sets for the first time. A novel algorithm is established to obtain …

The space–time fractional Telegraph equation and the space–time fractional modified third-
order Kdv equations are significant molding equations in theoretic physics, mathematical …

This study is devoted to uncover the optical solitons and other solutions. The mathematical
models used for this purpose is Chen–Lee–Liu equation in birefringent fibers which consist …

The stochastic coupled Maccari's system (MS) is a kind of important nonlinear partial
differential equations to describe fluid flow, plasma physics, nonlinear optics and so on. In …

This work suggests a fractional modification of the KdV–Kadomtsev–Petviashvili model with
the beta-derivative to consider unsmooth boundary. Some new interesting solitary waves …

We present the modified simple equation method for solving nonlinear fractional-order
partial differential equations (fPDEs). With the presented method, some important fPDEs are …

In this pioneering study, we have systematically derived traveling wave solutions for the
highly intricate Zoomeron equation, employing well-established mathematical frameworks …