Some Remarks About Riemann-Liouville and Caputo Impulsive Fractional Calculus

Authors: M. De la Sen

Abstract:

This paper establishes some closed formulas for Riemann- Liouville impulsive fractional integral calculus and also for Riemann- Liouville and Caputo impulsive fractional derivatives.

Keywords: Rimann- Liouville fractional calculus, Caputofractional derivative, Dirac delta, Distributional derivatives, Highorderdistributional derivatives.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072239

References:

[1] O. Y. Luchko and R. Gorenflo, "An operational method for solving fractional differential equations with the Caputo derivatives", Acta Mathematica Vietnamica, Vol. 24, No. 2 , pp. 207-233, 1999.
[2] Yu. F. Luchko and H.M. Srivastava, "Differential equations of fractional order by using operational calculus", Computers and Mathematics with Applications, Vol. 29, No. 8 , pp. 73-85, 1995.
[3] K. Oldham and J. Spanier, The fractional Calculus. Theory and Applications of Differentiation and Integration to Arbitrary Order, Dover Publications INC, Mineola, New York, 1974.
[4] S. Das, Functional Fractional calculus for System Identification and Controls, Springer-Verlag, Berlin, 2008.
[5] L.A. Zadeh and C. A. Desoer, Linear System Theory, McGraw- Hill, New York, 1963.
[6] M. De la Sen, "A method for general design of positive real functions", IEEE Transaction on Circuits and Systems I-Fundamental Theory and Applications, Vol. 45, no. 7, pp. 764-769, 1998, doi:10.1109/81.703845.
[7] M. Delasen, "A method for general design of positive real functions", International Journal of Control, Vol. 41, no. 5, pp. 1189-1205, 1985, doi: 10.1080/0020718508961191.
[8] M. Delasen, "A method for general design of positive real functions", International Journal of Systems Science, Vol. 14, no. 4, pp. 367-383, 1983, doi: 10.1080/00207728308926464.
[9] N. Luo, J. Rodellar , J. Vehi and M. De la Sen, "Composite semiactive control of seismically excited structures", Journal of the Franklin Institute- Engineering and Applied Mathematics, Vol. 338, No. 2-3, pp. 764-769, 2001, doi: 10.1016/S0016-0032(00)00081-8.