The primary aim of this manuscript is to present the approximate analytical solutions of the time fractional order α (1<α≤2) Vibration Equation (VE) of large membranes with the use of an iterative technique namely Residual Power Series Method (RPSM). The fractional derivative is defined in the Caputo sense. Example problems have been solved to demonstrate the efficacy of the present method and ...

In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modified Weibull-p...

In the present article, fractional order differential difference equation is solved by using residual power series method. Residual method solutions for classical and are obtained in a form showing good accuracy of Illustrative models considered to affirm legitimacy technique. The chosen problems represented tables plots which show between exact assimilated models.

In this article a new approach in solving time fractional partial differential equations is introduced, that is, the ARA-residual power series method. The main idea of technique, depends on applying ARA-transform and using Taylor's expansion to construct approximate solutions. procedure getting solutions for nonlinear difficult mission, method over comes trouble throughout expressing solution f...

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.

This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination transformation and technique, we achieve analytic approximation results in rapid convergent form by employing notion limit, with less time effort than method. Three challen...