Abstract
Systems with generalized two-terms fractional difference operators are discussed. By the choice of a certain kernel, these operators can be reduced to the standard fractional integrals and derivatives. We study existence of solutions to such systems.
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References
Agrawal, O.P., Tenreiro-Machado, J.A., Sabatier, J.: Fractional Derivatives and Their Application: Nonlinear Dynamics, vol. 38. Springer, Berlin (2004)
Abdeljawad, T., Baleanu, D.: Fractional differences and integration by parts. Journal of Computational Analysis and Applications 13(3), 574–582 (2011)
Atici, F.M., Eloe, P.W.: Initial value problems in discrete fractional calculus. Proceedings of the American Mathematical Society (2008), S 0002-9939(08)09626-3
Atici, F.M., Eloe, P.W.: A Transform Method in Discrete Fractional Calculus. International Journal of Difference Equations 2, 165–176 (2007)
Bastos, N.R.O., Ferreira, R.A.C., Torres, D.F.M.: Necessary optimality conditions for fractional difference problems of the calculus of variations. Discrete Contin. Dyn. Syst. 29(2), 417–437 (2011)
Chen, F., Luo, X., Zhou, Y.: Existence results for nonlinear fractional difference equation. Advances in Difference Eq., article ID 713201, 12 (2011), doi:10.1155/2011/713201
Mozyrska, D., Girejko, E.: Overview of the fractional h-difference operators. In: Almeida, A., Castro, L., Speck, F.O. (eds.) Advances in Harmonic Analysis and Operator Theory – The Stefan Samko Anniversary Volume, Operator Theory: Advances and Applications, vol. 229, XII, 388 p. Birkhäuser (2013) ISBN: 978-3-0348-0515-5
Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Signapore (2000)
Holm, M.T.: The theory of discrete fractional calculus: Development and application. University of Nebraska, Lincoln (2011)
Basik, M., Klimek, M.: On application of contraction principle to solve two-term fractional differential equations. Acta Mechanica et Automatica 5(2), 5–10 (2011)
Magin, R.L.: Fractional Calculus in Bioengineering. Begell House Publisher, Redding (2006)
Miller, K.S., Ross, B.: Fractional difference calculus. In: Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and their Applications, pp. 139–152. Nihon University, Kōriyama (1988)
Mozyrska, D., Pawłuszewicz, E.: Controllability of h-difference linear control systems with two fractional orders. Submitted to 13th International Carpathian Control Conference, ICCC 2012, Slovak Republik, May 28-31 (2012) (to appear)
Ortigueira, M.D.: Fractional discrete-time linear systems. In: Proc. of the IEE-ICASSP 1997, Munich, Germany, vol. 3, pp. 2241–2244. IEEE, New York (1997)
Podlubny, I.: Fractional Differential Equations. AP, New York (1999)
West, B.J., Bologna, M., Grigolini, P.: Physics of Fractional Operators. Springer, Berlin (2003)
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Girejko, E., Mozyrska, D., Wyrwas, M. (2013). Solutions of Systems with Two-Terms Fractional Difference Operators. In: Mitkowski, W., Kacprzyk, J., Baranowski, J. (eds) Advances in the Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 257. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00933-9_16
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DOI: https://doi.org/10.1007/978-3-319-00933-9_16
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