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International GeoGebra Conference for Southeast Europe January 15-16, Novi Sad, Serbia

International GeoGebra Conference for Southeast Europe January 15-16, Novi Sad, Serbia. Fractional calculus and Geogebra Đurđica Takači Departman za matematiku i informatiku Prirodno-matemati čki fakultet Univerzitet u Novom Sadu. Gamma Function.

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International GeoGebra Conference for Southeast Europe January 15-16, Novi Sad, Serbia

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  1. International GeoGebra Conference for Southeast EuropeJanuary 15-16, Novi Sad, Serbia Fractional calculus and Geogebra Đurđica Takači Departman za matematiku i informatiku Prirodno-matematički fakultet Univerzitet u Novom Sadu

  2. Gamma Function Gamma function extends factorials to non-integervalues GamaFunkcija Gamma function extends factorials to non-integervalues GamaFunkcija

  3. Convolution Convolution of two functions Convolution.ggb

  4. On the power (order) of the derivative -- differential operator The origins of the fractional calculus go back to the end of the 17th century, when L'Hospital asked (in a letter) Leibniz about the sense of the notation the derivative of order 1/2. Leibniz's answer was "An apparent paradox, from which one day useful consequences will be drawn."

  5. Fractional calculus is a natural generalization of calculus Many applications of fractional calculus in: viscoelasticity and damping, diffusion and wave propagation, electromagnetism, chaos and fractals, heat transfer, biology, electronics, signal processing, robotics, system identification, traffic systems, genetic algorithms, percolation, modeling and identification, telecommunications, chemistry, irreversibility, physics, control systems, economy, and finance,...

  6. Fractional calculus Rimann-Liouville fractional integral operator of order Fractional-Integral

  7. Fractional derivatives in Caputo sense • Fractional Derivative

  8. Fractional derivatives in Caputo sense Fractional Derivative

  9. Delta Functions The Dirac delta function, or δ function(introduced by Paul Dirac), is a generalized function: Delta sequences Academ. Stevan Pilipovic

  10. References:1. Caputo, M., Linear models of dissipation whose Q is almost frequency independent- II,Geophys. J. Royal Astronom. Soc., 13, No 5 (1967), 529-539 2. Mainardi, F., Yu. Luchko, Pagnini, G., The fundamental solution ofthe space-time fractional diffusion equation Fractional Calculus and its Application, 4,2. 2001, 153-192. 3. Mainardi, F., Pagnini, G., The Wright functions asthe solutions of time-fractional diffusion equation Applied Math. and Comp.Vol.141,Iss.1, 20 August 2003, 51-62. 4. Podlubny, I., Fractional Differential Equations, Acad.Press, San Diego (1999). 5. Ross, B., A brief history and exposition of fundamental theoryof fractional calculus, In: "Fractional Calculus and ItsApplications" (Proc. 1st Internat. Conf. held in New Haven, 1974;Lecture Notes in Math. 457, Springer-Verlag, N. York(1975), pp. 1-37. 6. Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integralsand Derivatives: Theory and Applications, Gordon and Breach Sci.Publ., Switzerland (1993).

  11. 7. Takači, Dj., Takači, A., On the approximate solution of mathematical model of a viscoelasticbar, Nonlinear Analysis, 67 (2007), 1560-1569. 8. Takači, Dj., Takači, A., On the mathematical model of a viscoelastic bar, Math. Meth. Appl. Sci. 2007; 30:1685-1695. 9. Yulita M. R., Noorani,M.S.M., Hashim, I. Variational iteration method for fractional heat- andwave-like equations, Nonlinear Analysis, 10 (2009), 1854-1869. 10. Odibat Z., M. Analytic study on linear systems of fractional differentialequations, Computers and Mathematics with Applications

  12. Delta Functions The Dirac delta function, or δ function(introduced by Paul Dirac), is a generalized function: Academician Stevan Pilipovic Delta sequences

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