6533b7d1fe1ef96bd125d752

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Fractional differential equations solved by using Mellin transform

Mario Di PaolaSalvatore Butera

subject

Numerical AnalysisMellin transformApplied MathematicsMathematical analysisRamanujan's master theoremIntegral equationFractional differential equationFractional calculusWiener–Hopf methodsymbols.namesakeMathematics - Analysis of PDEsSelf-similarity of inverse Mellin transform.Modeling and SimulationLaplace transform applied to differential equationssymbolsMellin inversion theoremFOS: MathematicsTwo-sided Laplace transformMellin transformMathematicsAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2014-01-01
10.1016/j.cnsns.2013.11.022http://arxiv.org/abs/1402.5949