let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power series in the Caputo derivatives sense. To illustrate the reliability of method some examples are provided. In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power...

In this paper, an integration of a symbolic power series method - Padé approximation technique (PS - Padé), was utilized to solve a system of nonlinear differential equations arising from the similarity solution of laminar thermal boundary layer over a flat plate subjected to a convective surface boundary condition. As both boundary conditions tended to infinity, the combination of series solut...

in this paper, an integration of a symbolic power series method - padé approximation technique (ps - padé), was utilized to solve a system of nonlinear differential equations arising from the similarity solution of laminar thermal boundary layer over a flat plate subjected to a convective surface boundary condition. as both boundary conditions tended to infinity, the combination of series solut...

In this work, power-series solutions of compartmental epidemiological models are used to provide alternate methods solve the corresponding systems nonlinear differential equations. A simple and classical SIR model is considered reveal clearly idea our approach. Moreover, a SAIRP also analyzed by using same methodology, previously applied COVID-19 pandemic. Numerical experiments perfo...

In this paper, a nonlinear stiff differential equation is solved by using the Rosenbrock iterative method, modified homotpy analysis method and power series method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relations. Some numerical examples are studied to demonstrate the accuracy of the presented meth...

Abstract Using a series of fractional powers we present representation the solution to logistic equation is presented. To simplify consider simplest case and prove that power indeed exact solution. Some numerical approximations are presented show good obtained by truncating series.