Fractional differential equations solved by using Mellin transform

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• 作者：Salvatore Butera ; Mario Di Paola
• 关键词：Fractional differential equations ; Mellin transform ; Self-similarity of inverse Mellin transform
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：July, 2014
• 年：2014
• 卷：19
• 期：7
• 页码：2220-2227
• 全文大小：418 K

文摘

In this paper, the solution of the multi-order differential equations, by using Mellin transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin integral operates on the fractional derivatives, may be overcame. Then, the solution may be found for any fractional differential equation involving multi-order fractional derivatives (or integrals). The solution is found in the Mellin domain, by solving a linear set of algebraic equations, whose inverse transform gives the solution of the fractional differential equation at hands.