In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]
This article reports on the solutions of the time-fractional diffusion equation. It discusses the numerical analysis of the time-fractional diffusion equation by using the time fractional derivative in the Caputo sense of order. It provides the equation for the Wright function with the series that appears within the solution of the time-fractional diffusion equation.
The fluctuationlessness approximation gives powerful and easily utilizable solutions for a lot of applications of numerical analysis. For example, it helps us to create univariate numerical integration schemes which converge very rapidly. On the other hand, the space extension approaches aim to convert equations into some other structures which can be handled more easily. It is possible to apply this approach to the solutions obtained with fluctuationlessness approximation in order to improve the quality of approximation. [ABSTRACT FROM AUTHOR]