No abstract

This paper introduces a new analytical technique (NAT) for solving a system of nonlinear fractional partial differential equations (NFPDEs) in full general set. Moreover, the convergence and error analysis of the proposed technique is shown. The approximate solutions for a system of NFPDEs are easily obtained by means of Caputo fractional partial derivatives based on the properties of fractional calculus. However, analytical and numerical traveling wave solutions for some systems of nonlinear wave equations are successfully obtained to confirm the accuracy and efficiency of the proposed technique. Several numerical results are presented in the format of tables and graphs to make a comparison with results previously obtained by other well-known methods Keywords: system of nonlinear fractional partial differential equations (NFPDEs); systems of nonlinear wave equations; new analytical technique (NAT); existence theorem; error analysis; approximate solution

This paper introduces advances in solving space‐time conformable nonlinear partial differential equations (PDEs) and exact wave solutions for Oskolkov equations. To arrive at these advances, nonlinear PDEs with space and time conformable partial derivatives are reduced to differential equations with conformable derivatives by using new modifications of the exponential rational function method (ERFM). These modifications are efficious approaches for obtaining exact analytical solutions. An important result of this work is that it yields new exact wave solutions for space‐time conformable pseudo‐parabolic type equations. The graphical representations of the obtained solutions are shown to confirm the accuracy and efficiency of the suggested method.

This paper introduces a new modification of least squares homotopy perturbation method (LSHPM) for solving linear and nonlinear fractional partial differential equations (FPDEs). The main advantage of the new modification is to approximate the solution for FPDEs in a full general set. Moreover, the convergence of the proposed modification is shown. Analytical and numerical solutions for the linear Navier-Stokes equation and the nonlinear gas dynamic equation are successfully obtained to confirm the accuracy and efficiency of the proposed modification.