Fractional Integration and Certain Dual Integral Equations.
Roop Narain Kesarwani (1967)
Mathematische Zeitschrift
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Displaying similar documents to “Correction to Fractional Integration and Certain Dual Integral Equations. Math. Zeitschr. 98, 83-88 (1967).”
Fractional Integration and Certain Dual Integral Equations.
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We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for...
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In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case...