Analytical techniques for solving the equation governing the unsteady flow of a polytropic gas with time-fractional derivative

Abstract

In this work, some analytical techniques viz. homotopy perturbation method, new iterative method and integral iterative method are used to solve nonlinear fractional differential equations such as the equation governing the unsteady flow of a polytropic gas with time-fractional derivative. Comparisons are made between the considered techniques and also between their results. The obtained results reveal that these techniques are very simple and effective and give the solution in series form which in closed form gives the exact solution also, reveal that the integral iterative technique is simpler and shorter in its computational procedures and time than the other techniques.

Asymptotic stability analysis of Riemann-Liouville fractional stochastic neutral differential equations

“…Based on average dwell-time method, Razumikhin-type technique and vector Lyapunov function, some novel stability method are obtained for impulsive stochastic functional differential systems. On a study of different types of stability studies for FSDEs can be found in [1,4,10,17,24,30,44].…”

Asymptotic stability analysis of Riemann-Liouville fractional stochastic neutral differential equations

“…Based on average dwell-time method, Razumikhin-type technique and vector Lyapunov function, some novel stability method are obtained for impulsive stochastic functional differential systems. On a study of different types of stability studies for FSDEs can be found in [2,3,4,5,24,44,45].…”