![]() īabenko, Yu.I.: Heat and Mass Transfer, Chimia, Leningrad 1986. Ĭaputo, M.: Elasticità e Dissipazione, Zanichelli, Bologna 1969. 1, Academic Press, New York 1964.ĭzherbashian, M.M.: Integral Transforms and Representations of Functions in the Complex Plane, Nauka, Moscow 1966. (Editor): Tables of Integral Transforms,Bateman Project, Vols. ![]() Rubin, B.: Fractional Integrals and Potentials, Pitman Monographs and Surveys, in Pure and Applied Mathematics #82, Addison Wesley Longman, Harlow 1996.ĭavis, H.T.: The Theory of Linear Operators, The Principia Press, Bloomington, Indiana 1936.Įrdélyi, A. (Editor): Boundary Value Problems, Special Functions and Fractional Calculus, Byelorussian State University, Minsk 1996. Kiryakova (Editors): Transform Methods and Spe-cial Functions, Sofia 1994, Science Culture Technology, Singapore 1995. Kiryakova, V.: Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics # 301, Longman, Harlow 1994. Ross: An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York 1993. (Editor): Recent Advances in Fractional Calculus, Global Publ., Sauk Rapids, Minnesota 1993. Nishimoto, K.: An Essence of Nishimoto’s Fractional Calculus, Descartes Press, Koriyama 1991. (Editor): Fractional Calculus and its Applications, Nihon University, Tokyo 1990. Owa (Editors): Univalent Functions, Fractional Calculus, and their Applications, Ellis Horwood, Chichester 1989. Marichev: Fractional Integrals and Derivatives,: Theory and Applications, Gordon and Breach, Amsterdam 1993. Roach (Editors): Fractional Calculus, Pitman Research Notes in Mathematics # 138, Pitman, London 1985. McBride, A.C.: Fractional Calculus and Integral Transforms of Generalized Functions, Pitman Research Notes in Mathematics # 31, Pitman, London 1979. Spanier: The Fractional Calculus, Academic Press, New York 1974. ![]() (Editor): Fractional Calculus and its Applications, Lecture Notes in Mathematics # 457, Springer Verlag, Berlin 1975. 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. We shall show the fundamental role of the Mittag-Leffler function, whose properties are reported in an ad hoc Appendix. By applying this technique we shall derive the analy ical solutions of the most simple linear integral and differential equations of fractional order. 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. In these lectures we introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |