Search results for "Wiener–Hopf method"

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Fractional differential equations solved by using Mellin transform

2014

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.

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)
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Mellin transform approach for the solution of coupled systems of fractional differential equations

2015

In this paper, the solution of a multi-order, multi-degree-of-freedom fractional differential equation is addressed by using the Mellin integral transform. By taking advantage of a technique that relates the transformed function, in points of the complex plane differing in the value of their real part, the solution is found in the Mellin domain by solving a linear set of algebraic equations. The approximate solution of the differential (or integral) equation is restored, in the time domain, by using the inverse Mellin transform in its discretized form.

Numerical AnalysisMellin transformLaplace transformApplied MathematicsMathematical analysisMulti degree of freedom systemsRamanujan's master theoremIntegral equationFractional differential equationWiener–Hopf methodsymbols.namesakeModeling and SimulationLaplace transform applied to differential equationsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONsymbolsMellin inversion theoremTwo-sided Laplace transformMellin transformMathematicsCommunications in Nonlinear Science and Numerical Simulation
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