On stretched magnetic surfaces, we present a numerical study of Casson nanofluids moving through porous materials. The Casson liquid model explains how non-Newtonian liquids behave. Numerical techniques are utilized to solve the nonlinear partial differential equations produced by similarity transformations. Results are gathered for the Nusselt number, skin friction coefficient, temperature and velocity. The impacts of physical variables on the flow and heat transfer characteristics of nanofluids are depicted in graphs. They include the Prandtl number, magnetic parameter, radiation parameter, porosity parameter and Casson parameter. Findings indicate that as the Casson nanofluid parameters are increased, the temperature profile rises but the velocity field decreases. With increasing magnetic parameters alone, it is possible to see a decrease in the thickness of the pulse boundary layer and an increase in the thickness of the thermal boundary layer. All the results are depicted in graphical representations.

In this article, the Korteweg-de Vries-Caudrey-Dodd-Gibbon (KdV-CDG) equation is explored via a fractional operator. A nonlocal differential operator with a nonsingular kernel is used to study the KdV-CDG equation. Some theoretical features concerned with the existence and uniqueness of the solution, convergence, and Picard-stability of the solution by using the concepts of fixed point theory are discussed. Analytical solutions of the KdV-CDG equation by using the Laplace transformation (LT) associated with the Adomian decomposition method (ADM) are retrieved. The solutions are presented using 3D and surface graphics.

The current manuscript focuses on the solution and analysis of space and time fractional coupled Schrödinger system that belongs to a class of evolution equations. These systems encounter in different fields related to plasma waves, optics, and quantum physics. The fractional He-Laplace approach is proposed for the series form solutions of fractional systems. This approach contains hybrid of Laplace transform and homotopy perturbation along with Caputo fractional derivative. The current study provide new results on time and space fractional coupled Schrödinger systems which are not captured in existing literature. Reliability of proposed algorithm in both time and space fractional scenarios is observed through residual error concept throughout fractional domains. The effect of fractional parameters on wave profiles are analyzed numerically and graphically as 2D and 3D illustrations. Analysis reveals that proposed algorithm is suitable for non-linear time-space fractional systems encountering in different fields of sciences.