On Solutions to Fractional Discrete Systems with Sequential h-Differences
We study the subject of a behaviour of the solutions of systems with sequential fractional h-differences. We give formulas for the unique solutions to initial value problems for systems in linear and semilinear cases. Moreover, the sufficient condition that guaranties the positivity of considered sy...
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| Published in | Abstract and Applied Analysis Vol. 2013; no. 2013; pp. 433 - 443-554 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Limiteds
01.01.2013
Hindawi Puplishing Corporation Hindawi Publishing Corporation John Wiley & Sons, Inc Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1085-3375 1687-0409 |
| DOI | 10.1155/2013/475350 |
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| Abstract | We study the subject of a behaviour of the solutions of systems with sequential fractional h-differences. We give formulas for the unique solutions to initial value problems for systems in linear and semilinear cases. Moreover, the sufficient condition that guaranties the positivity of considered systems is presented. |
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| AbstractList | We study the subject of a behaviour of the solutions of systems with sequential fractional
h
-differences. We give formulas for the unique solutions to initial value problems for systems in linear and semilinear cases. Moreover, the sufficient condition that guaranties the positivity of considered systems is presented. We study the subject of a behaviour of the solutions of systems with sequential fractional h-differences. We give formulas for the unique solutions to initial value problems for systems in linear and semilinear cases. Moreover, the sufficient condition that guaranties the positivity of considered systems is presented. |
| Audience | Academic |
| Author | Mozyrska, Dorota Girejko, Ewa Wyrwas, Małgorzata |
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| CitedBy_id | crossref_primary_10_1155_2020_3085036 crossref_primary_10_1016_j_cnsns_2017_01_002 crossref_primary_10_1142_S021812742150245X crossref_primary_10_1186_s13662_018_1793_6 |
| Cites_doi | 10.1007/978-3-319-00933-9_6 10.1007/978-3-0348-0516-2_14 10.1108/03684920910976826 10.1090/S0002-9939-08-09626-3 10.1186/1687-1847-2013-36 10.1016/j.camwa.2011.03.036 10.1016/j.sigpro.2010.05.001 10.2478/s11534-013-0223-3 10.1155/2011/713201 10.2478/v10006-009-0008-4 10.1016/j.cnsns.2011.01.018 10.2298/AADM110131002F 10.1007/978-3-319-00933-9_17 10.2478/bpasts-2013-0024 10.1155/2013/406910 10.1155/2013/104173 10.3934/dcds.2011.29.417 10.1007/978-3-319-00933-9_4 10.1186/1687-2770-2012-58 10.1080/00207721.2013.794907 10.1080/00207179.2011.643413 10.1155/2012/476581 10.2478/v10006-008-0020-0 10.3166/JESA.42.769-787 |
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| Contributor | Mozyrska, Dorota Girejko, Ewa |
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| Copyright | Copyright © 2013 Małgorzata Wyrwas et al. COPYRIGHT 2014 John Wiley & Sons, Inc. Copyright © 2013 Malgorzata Wyrwas et al. Malgorzata Wyrwas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright 2013 Hindawi Publishing Corporation |
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| References | (26) 2011; 16 (8) 2008; 18 Kaczorek T. Selected Problems of Fractional Systems Theory 2011 411 Berlin, Germany Springer (16) 2011; 5 Ortigueira M. D. Fractional discrete-time linear systems 3 Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97) 1997 Munich, Germany IEEE Computer Society 2241 2244 10.1109/ICASSP.1997.599497 (31) 2009; 19 (3) 2007; 2 (30) 2009; 38 Mozyrska D. Girejko E. Overview of the fractional h-difference operators Advances in Harmonic Analysis and Operator Theory 2013 229 New York, NY, USA Springer 253 268 Operator Theory: Advances and Applications 10.1007/978-3-0348-0516-2_14 MR3060418 (6) 2011; 2011 Pawluszewicz E. Mozyrska D. Mitkowski W. Kacprzyk J. Baranowski J. Constrained controllability of h-difference linear systems with two fractional orders Advances in the Theory and Applications of Non-Integer Order Systems 2013 257 New York, NY, USA Springer 67 75 Lecture Notes in Electrical Engineering 10.1007/978-3-319-00933-9_6 Wyrwas M. Girejko E. Mozyrska D. Pawłuszewicz E. Mitkowski W. Kacprzyk J. Baranowski J. Stability of fractional difference systems with two orders Advances in the Thoery and Applications of Non-Integer Order Systems 2013 257 New York, NY, USA Springer 41 52 Lecture Notes in Electrical Engineering 10.1007/978-3-319-00933-9_4 (27) 2012; 2012 Mozyrska D. Girejko E. Wyrwas M. Mitkowski W. Kacprzyk J. Baranowski J. Comparison of h-difference fractional operators Advances in the Thoery and Applications of Non-Integer Order Systems 2013 257 New York, NY, USA Springer 191 197 Lecture Notes in Electrical Engineering (5) 2011; 91 (2) 2011; 13 (14) 2013; 2013 (29) 2008; 42 Holm M. T. The theory of discrete fractional calculus: development and application [Ph.D. thesis] 2011 Lincoln, Neb, USA University of Nebraska (13) 2013; 2013 (22) 2013 (1) 1997; 27 (33) 2011; 62 Miller K. S. Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 1st New York, NY, USA John Wiley & Sons MR1219954 (17) 2011; 29 (21) 2013; 61 Miller K. S. Ross B. Fractional difference calculus Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications 1988 Kōriyama, Japan Nihon University 139 152 Podlubny I. Fractional Differential Equations 1999 San Diego, Calif, USA Academic Press MR1658022 (18) 2012; 85 (4) 2009; 137 (15) 2013; 2013 (20) 2012; 2012 (28) 2013 22 23 24 26 27 28 29 (19) 2013; 257 30 31 10 33 13 14 (25) 1993 15 16 (32) 2011; 411 17 18 4 5 6 8 (12) 1999 20 21 |
| References_xml | – reference: Kaczorek T. Selected Problems of Fractional Systems Theory 2011 411 Berlin, Germany Springer – volume: 85 start-page: 213 issue: 2 year: 2012 end-page: 219 ident: 18 article-title: Fractional discrete-time linear control systems with initialisation – volume: 16 start-page: 4689 issue: 12 year: 2011 end-page: 4697 ident: 26 article-title: Sequential fractional differential equations with hadamard derivative – volume: 5 start-page: 110 issue: 1 year: 2011 end-page: 121 ident: 16 article-title: Fractional -difference equations arising from the calculus of variations – volume: 27 start-page: 107 issue: 2-3 year: 1997 end-page: 122 ident: 1 article-title: Analysis and design of fractional-order digital control systems – volume: 29 start-page: 417 issue: 2 year: 2011 end-page: 437 ident: 17 article-title: Necessary optimality conditions for fractional difference problems of the calculus of variations – volume: 62 start-page: 1602 issue: 3 year: 2011 end-page: 1611 ident: 33 article-title: On Riemann and Caputo fractional differences – reference: Holm M. T. The theory of discrete fractional calculus: development and application [Ph.D. thesis] 2011 Lincoln, Neb, USA University of Nebraska – volume: 42 start-page: 769 issue: 6–8 year: 2008 end-page: 787 ident: 29 article-title: Reachability and controllability to zero tests for standard and positive fractional discrete-time systems – volume: 2013 year: 2013 end-page: 6 ident: 15 article-title: Fractional sums and difference with binomial coefficients – volume: 2011 year: 2011 end-page: 12 ident: 6 article-title: Existence results for nonlinear fractional difference equation – volume: 91 start-page: 513 issue: 3 year: 2011 end-page: 524 ident: 5 article-title: Discrete-time fractional variational problems – volume: 2012 year: 2012 end-page: 9 ident: 20 article-title: On the stability of some discrete fractional nonautonomous systems – reference: Miller K. S. Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 1st New York, NY, USA John Wiley & Sons MR1219954 – volume: 18 start-page: 223 issue: 2 year: 2008 end-page: 228 ident: 8 article-title: Fractional positive continuous-time linear systems and their reachability – volume: 61 start-page: 251 issue: 1 year: 2013 end-page: 256 ident: 21 article-title: Local controllability of nonlinear discrete-time fractional order systems – volume: 2012 year: 2012 ident: 27 article-title: A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions – volume: 2013 year: 2013 ident: 13 article-title: Dual identities in fractional difference calculus within Riemann – reference: Ortigueira M. D. Fractional discrete-time linear systems 3 Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97) 1997 Munich, Germany IEEE Computer Society 2241 2244 10.1109/ICASSP.1997.599497 – volume: 19 start-page: 89 issue: 1 year: 2009 end-page: 93 ident: 31 article-title: Reachability of cone fractional continuous-time linear systems – volume: 137 start-page: 981 issue: 3 year: 2009 end-page: 989 ident: 4 article-title: Initial value problems in discrete fractional calculus – reference: Mozyrska D. Girejko E. Wyrwas M. Mitkowski W. Kacprzyk J. Baranowski J. Comparison of h-difference fractional operators Advances in the Thoery and Applications of Non-Integer Order Systems 2013 257 New York, NY, USA Springer 191 197 Lecture Notes in Electrical Engineering – reference: Pawluszewicz E. Mozyrska D. Mitkowski W. Kacprzyk J. Baranowski J. Constrained controllability of h-difference linear systems with two fractional orders Advances in the Theory and Applications of Non-Integer Order Systems 2013 257 New York, NY, USA Springer 67 75 Lecture Notes in Electrical Engineering 10.1007/978-3-319-00933-9_6 – volume: 2 start-page: 165 issue: 2 year: 2007 end-page: 176 ident: 3 article-title: A transform method in discrete fractional calculus – reference: Wyrwas M. Girejko E. Mozyrska D. Pawłuszewicz E. Mitkowski W. Kacprzyk J. Baranowski J. Stability of fractional difference systems with two orders Advances in the Thoery and Applications of Non-Integer Order Systems 2013 257 New York, NY, USA Springer 41 52 Lecture Notes in Electrical Engineering 10.1007/978-3-319-00933-9_4 – reference: Mozyrska D. Girejko E. Overview of the fractional h-difference operators Advances in Harmonic Analysis and Operator Theory 2013 229 New York, NY, USA Springer 253 268 Operator Theory: Advances and Applications 10.1007/978-3-0348-0516-2_14 MR3060418 – volume: 2013 year: 2013 end-page: 12 ident: 14 article-title: On delta and nabla Caputo fractional differences and dual identities – year: 2013 ident: 28 article-title: Fractional nonlinear systems with sequential operators – volume: 13 start-page: 574 issue: 3 year: 2011 end-page: 582 ident: 2 article-title: Fractional differences and integration by parts – volume: 38 start-page: 1059 issue: 7-8 year: 2009 end-page: 1078 ident: 30 article-title: Fractional positive linear systems – year: 2013 ident: 22 article-title: Controllability of -difference linear control systems with two fractional orders – reference: Miller K. S. Ross B. Fractional difference calculus Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications 1988 Kōriyama, Japan Nihon University 139 152 – reference: Podlubny I. Fractional Differential Equations 1999 San Diego, Calif, USA Academic Press MR1658022 – ident: 23 doi: 10.1007/978-3-319-00933-9_6 – ident: 10 doi: 10.1007/978-3-0348-0516-2_14 – ident: 30 doi: 10.1108/03684920910976826 – volume: 13 start-page: 574 issue: 3 year: 2011 ident: 2 publication-title: Journal of Computational Analysis and Applications – volume: 2 start-page: 165 issue: 2 year: 2007 ident: 3 publication-title: International Journal of Difference Equations – ident: 4 doi: 10.1090/S0002-9939-08-09626-3 – ident: 13 doi: 10.1186/1687-1847-2013-36 – ident: 33 doi: 10.1016/j.camwa.2011.03.036 – ident: 5 doi: 10.1016/j.sigpro.2010.05.001 – ident: 28 doi: 10.2478/s11534-013-0223-3 – ident: 6 doi: 10.1155/2011/713201 – ident: 31 doi: 10.2478/v10006-009-0008-4 – ident: 26 doi: 10.1016/j.cnsns.2011.01.018 – ident: 16 doi: 10.2298/AADM110131002F – volume: 257 start-page: 191 volume-title: Comparison of h-difference fractional operators year: 2013 ident: 19 doi: 10.1007/978-3-319-00933-9_17 – year: 1993 ident: 25 – ident: 21 doi: 10.2478/bpasts-2013-0024 – ident: 14 doi: 10.1155/2013/406910 – ident: 15 doi: 10.1155/2013/104173 – ident: 17 doi: 10.3934/dcds.2011.29.417 – ident: 24 doi: 10.1007/978-3-319-00933-9_4 – ident: 27 doi: 10.1186/1687-2770-2012-58 – year: 1999 ident: 12 – ident: 22 doi: 10.1080/00207721.2013.794907 – volume: 27 start-page: 107 issue: 2-3 year: 1997 ident: 1 publication-title: Systems Analysis Modelling Simulation – ident: 18 doi: 10.1080/00207179.2011.643413 – ident: 20 doi: 10.1155/2012/476581 – ident: 8 doi: 10.2478/v10006-008-0020-0 – ident: 29 doi: 10.3166/JESA.42.769-787 – volume: 411 year: 2011 ident: 32 |
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| Snippet | We study the subject of a behaviour of the solutions of systems with sequential fractional h-differences. We give formulas for the unique solutions to initial... We study the subject of a behaviour of the solutions of systems with sequential fractional h -differences. We give formulas for the unique solutions to initial... We study the subject of a behaviour of the solutions of systems with sequential fractional h -differences. We give formulas for the unique solutions to initial... |
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| Title | On Solutions to Fractional Discrete Systems with Sequential h-Differences |
| URI | https://www.airitilibrary.com/Article/Detail/P20160825001-201312-201609070065-201609070065-433-443-554 https://search.emarefa.net/detail/BIM-474519 https://dx.doi.org/10.1155/2013/475350 https://www.proquest.com/docview/1564233607 http://projecteuclid.org/euclid.aaa/1393450243 https://doaj.org/article/f831f3ab77be4348b9d9a024408b7fa3 |
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