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1. On Genocchi Operational Matrix of Fractional Integration for Solving Fractional Differential Equations.

Author

Abdulnasir Isah and Chang Phang

Subjects
*FRACTIONAL integrals, *MATHEMATICS, *POLYNOMIALS, *MATHEMATICAL analysis, *NUMERICAL analysis, *EQUATIONS, *ALGEBRA
Abstract

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]

Published
2017
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2. An extension of the Derrida–Lebowitz–Speer–Spohn equation.

Author

Charles Bordenave, Pierre Germain, and Thomas Trogdon

Subjects
*EQUATIONS, *NUMERICAL analysis, *ALGEBRA, *MATHEMATICS, *MATHEMATICAL analysis
Abstract

We show how the derivation of the Derrida–Lebowitz–Speer–Spohn equation can be prolonged to obtain a new equation, generalizing the models obtained in the paper by these authors. We then investigate its properties from both an analytical and numerical perspective. Specifically, a numerical method is presented to approximate solutions of the prolonged equation. Using this method, we investigate the relationship between the solutions of the prolonged equation and the Tracy–Widom GOE distribution. [ABSTRACT FROM AUTHOR]

Published
2015
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