Series solution of fractional Pantograph equations via Taylor series

The Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential ‎Equations

‎This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert space. This method cannot be used directly to solve these equations, so an equivalent transformation is made by u...

Fractional Calculus and the Taylor-riemann Series

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...

The Taylor Method for Numerical Solution of Fuzzy Generalized Pantograph Equations with Linear Functional Argument

Neumann-Series Solution of Fractional Differential Equation

Approximate Series Solution of Nonlinear, Fractional Klein- Gordon Equations Using Fractional Reduced Differential Transform Method

Corresponding Author: Mohammed Al-Smadi Department of Applied Science, Ajloun College, AlBalqa Applied University, Ajloun 26816, Jordan Email: [email protected] Abstract: This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Red...