Necessary Conditions to Solve Fractional Order Wave Equations Using Traditional Laplace Transforms

Necessary Conditions to Solve Fractional Order Wave Equations Using Traditional Laplace Transforms

Maxwell’s equations modified for dielectric permittivity lead to a modified wave equation similar to the viscoelastic wave equation for solid materials. In the process of the modification, certain terms arise that do not have traditional Laplace transforms. This paper addresses the necessary conditi...

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Veröffentlicht in:Fractional calculus & applied analysis 2015-12, Vol.18 (6), p.1350-1357
Hauptverfasser: Wharmby, Andrew W., Bagley, Ronald L.
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Analysis
fractional calculus
fractional ordinary and partial differential equations
Functional Analysis
Integral Transforms
Laplace transforms
Leibniz integral rule
Mathematics
Operational Calculus
Short Paper
wave equation
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Beschreibung
Zusammenfassung:Maxwell’s equations modified for dielectric permittivity lead to a modified wave equation similar to the viscoelastic wave equation for solid materials. In the process of the modification, certain terms arise that do not have traditional Laplace transforms. This paper addresses the necessary conditions needed to remove these problematic terms from the analysis.
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2015-0078