The homotopy perturbation method (HPM) was proposed by Ji-Huan. He was a rising star in
analytical methods, and all traditional analytical methods had abdicated their crowns. It is …

Abstract The Riccati-Bernoulli sub-ODE method is firstly proposed to construct exact
traveling wave solutions, solitary wave solutions, and peaked wave solutions for nonlinear …

Time-fractional partial differential equations describe different phenomena in statistical
physics, applied mathematics, and engineering. In this article, we propose and analyze an …

In this paper, the fractional derivatives in the sense of modified Riemann–Liouville derivative
and the first integral method are employed for constructing the exact solutions of nonlinear …

In this article, we study the time‐fractional nonlinear Klein–Gordon equation in Caputo–
Fabrizio's sense and Atangana–Baleanu–Caputo's sense. The modified double Laplace …

In this study, the extended tanh-function method has been used to find further general
travelling wave solutions for space-time fractional nonlinear partial differential equations …

In this letter, we present a hybrid computational approach established on local fractional
Sumudu transform method and homotopy perturbation technique to procure the solution of …

In this paper, we implemented the functional variable method and the modified Riemann–
Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the …

In this paper, we propose a numerical method for the solution of time fractional nonlinear
sine-Gordon equation that appears extensively in classical lattice dynamics in the continuum …

The discrete gradient structure and the positive definiteness of discrete fractional integrals or
derivatives are fundamental to the numerical stability in long-time simulation of nonlinear …