Fractional Calculus: Integral and Differential Equations of Fractional Order

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dc.creatorGorenflo, Rudolf
dc.creatorMainardi, Francesco
dc.date2008-05-25
dc.date.accessioned2026-07-07T09:40:51Z
dc.date.available2026-07-07T09:40:51Z
dc.descriptionWe introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating these operators in a way accessible to applied scientists, avoiding unproductive generalities and excessive mathematical rigor. By applying this technique we shall derive the analytical solutions of the most simple linear integral and differential equations of fractional order. We show the fundamental role of the Mittag-Leffler function, whose properties are reported in an ad hoc Appendix. The topics discussed here will be: (a) essentials of Riemann-Liouville fractional calculus with basic formulas of Laplace transforms, (b) Abel type integral equations of first and second kind, (c) relaxation and oscillation type differential equations of fractional order.
dc.description56 pages, 7 figures/eps files
dc.identifierhttps://arxiv.org/abs/0805.3823
dc.identifierhttp://arxiv.org/abs/0805.3823
dc.identifierA. Carpinteri and F. Mainardi (Editors): Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien and New York 1997, pp. 223-276.,
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161622
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectComplex Variables
dc.subjectHistory and Overview
dc.subject26A33, 33E12, 33E20, 44A20, 45E10, 45J05
dc.titleFractional Calculus: Integral and Differential Equations of Fractional Order
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