The trajectory of fractional calculus has undergone several periods of intensive
development, both in pure and applied sciences. During the last few decades fractional …

A finite difference scheme which depends on a new approximation based on an extended
cubic B-spline for the second order derivative is used to calculate the numerical outcomes of …

In this article, the analytical solutions to the space-time fractional foam drainage equation
and the space-time fractional symmetric regularized long wave (SRLW) equation are …

The primary motivation of this paper is to extend the application of the reproducing-kernel
method (RKM) and the residual power series method (RPSM) to conduct a numerical …

Kee** in view of the complex fluid mechanics in bio-medicine and engineering, the
Burgers' fluid with a fractional derivatives model analyzed through a rotating annulus. The …

The space-time fractional-coupled Burgers equations and the space-time fractional foam
drainage equation are important as an electro-hydro-dynamical model to progress the local …

The ill-posedness of the forward-backward heat problem arises in boundary layer problems,
fluid dynamics, plasma physics, astrophysics and the study of propagation of an electron …

In this work, we want to use the Non-polynomial spline basis and Quasi-linearization method
to solve the nonlinear Volterra integral equation. When the iterations of the Quasilinear …

We apply the reproducing kernel method and group preserving scheme for investigating the
Lane–Emden equation. The reproducing kernel method is implemented by the useful …

Abstract The Sharma-Tasso-Olver and Klein–Gordon equations are significant models to
interpret plasma physics, relativistic physics, quantum mechanics, nonlinear optics, etc. In …