Tytuł artykułu
Autorzy
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper, controllability results for a class of multi-term time-fractional differential systems with state-dependent delay have been studied. The concept of fractional calculus, measure of noncompactness and Mönch fixed-point theorem has been implemented to obtain a new set of controllability results. Finally, an application is given to illustrate the obtained results.
Wydawca
Czasopismo
Rocznik
Tom
Strony
241--255
Opis fizyczny
Bibliogr. 45 poz.
Twórcy
autor
- Department of Mathematics, School of Basic and Applied Sciences, G D Goenka University, Gurugram, India
autor
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India
autor
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India
Bibliografia
- [1] E. Alvarez-Pardo and C. Lizama, Mild solutions for multi-term time-fractional differential equations with nonlocal initial conditions, Electron. J. Differential Equations 2014 (2014), Paper No. 39.
- [2] U. Arora and N. Sukavanam, Controllability of retarded semilinear fractional system with non-local conditions, IMA J. Math. Control Inform. 35 (2018), no. 3, 689-705.
- [3] K. Balachandran, V. Govindaraj, L. Rodríguez-Germa and J. J. Trujillo, Controllability results for nonlinear fractional-order dynamical systems, J. Optim. Theory Appl. 156 (2013), no. 1, 33-44.
- [4] K. Balachandran and J. Y. Park, Controllability of fractional integrodifferential systems in Banach spaces, Nonlinear Anal. Hybrid Syst. 3 (2009), no. 4, 363-367.
- [5] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes Pure Appl. Math. 60, Marcel Dekker, New York, 1980.
- [6] G. Barenblat, J. Zheltor and I. Kochiva, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech. 24 (1960), 1286-1303.
- [7] M. Bragdi and M. Hazi, Existence and controllability result for an evolution fractional integrodifferential systems, Int. J. Contemp. Math. Sci. 5 (2010), no. 17-20, 901-910.
- [8] D. Chalishajar, A. Annamalai, K. Malar and K. Kulandhivel, A study of controllability of impulsive neutral evolution integro-differential equations with state-dependent delay in Banach spaces, Mathematics 5 (2016), DOI 10.3390/math4040060.
- [9] R. Chaudhary and D. N. Pandey, Existence results for a class of impulsive neutral fractional stochastic integro-differential systems with state dependent delay, Stoch. Anal. Appl. 37 (2019), no. 5, 865-892.
- [10] R. Chokkalingam and B. Dumitru, On the controllability of fractional functional integro-differential systems with an infinite delay in Banach spaces, Adv. Difference Equ. 291 (2013), 1-13.
- [11] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
- [12] X. Fu and R. Huang, Existence of solutions for neutral integro-differential equations with state-dependent delay, Appl. Math. Comput. 224 (2013), 743-759.
- [13] G. R. Gautam and J. Dabas, Mild solution for nonlocal fractional functional differential equation with not instantaneous impulse, Int. J. Nonlinear Sci. 21 (2016), no. 3, 151-160.
- [14] M. Giona, S. Cerbelli and H. E. Roman, Fractional diffusion equation and relaxation in complex viscoelastic materials, Phys. A 191 (1992), 449-453.
- [15] D. Guo, V. Lakshmikantham and X. Liu, Nonlinear Integral Equations in Abstract Spaces, Math. Appl. 373, Kluwer Academic, Dordrecht, 1996.
- [16] J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), no. 1, 11-41.
- [17] E. Hernández, A. Prokopczyk and L. Ladeira, A note on partial functional differential equations with state-dependent delay, Nonlinear Anal. Real World Appl. 7 (2006), no. 4, 510-519.
- [18] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, River Edge, 2000.
- [19] Y. Hino, S. Murakami and T. Naito, Functional-differential Equations with Infinite Delay, Lecture Notes in Math. 1473, Springer, Berlin, 1991.
- [20] H. Jiang, F. Liu, I. Turner and K. Burrage, Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain, Comput. Math. Appl. 64 (2012), no. 10, 3377-3388.
- [21] Kamaljeet and D. Bahuguna, Approximate controllability of nonlocal neutral fractional integro-differential equations with finite delay, J. Dyn. Control Syst. 22 (2016), no. 3, 485-504.
- [22] M. Kamenskii, V. Obukhovskii and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, De Gruyter Ser. Nonlinear Anal. Appl. 7, Walter de Gruyter, Berlin, 2001.
- [23] V. Keyantuo, C. Lizama and M. Warma, Asymptotic behavior of fractional-order semilinear evolution equations, Differential Integral Equations 26 (2013), no. 7-8, 757-780.
- [24] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006.
- [25] J. Klamka, Controllability of Dynamical Systems, Math. Appl. (East European Series) 48, Kluwer Academic, Dordrecht, 1991.
- [26] F. Liu, M. M. Meerschaert, R. J. McGough, P. Zhuang and Q. Liu, Numerical methods for solving the multi-term time-fractional wave-diffusion equation, Fract. Calc. Appl. Anal. 16 (2013), no. 1, 9-25.
- [27] C. Lizama, An operator theoretical approach to a class of fractional order differential equations, Appl. Math. Lett. 24 (2011), no. 2, 184-190.
- [28] V. T. Luong, Decay mild solutions for two-term time fractional differential equations in Banach spaces, J. Fixed Point Theory Appl. 18 (2016), no. 2, 417-432.
- [29] J. A. Machado, C. Ravichandran, M. Rivero and J. J. Trujillo, Controllability results for impulsive mixed-type functional integro-differential evolution equations with nonlocal conditions, Fixed Point Theory Appl. 2013 (2013), Paper No. 66.
- [30] N. I. Mahmudov, Controllability of linear stochastic systems in Hilbert spaces, J. Math. Anal. Appl. 259 (2001), no. 1, 64-82.
- [31] N. I. Mahmudov and N. Şemi, Approximate controllability of semilinear control systems in Hilbert spaces, TWMS J. Appl. Eng. Math. 2 (2012), no. 1, 67-74.
- [32] F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in: Fractals and Fractional Calculus in Continuum Mechanics (Udine 1996), CISM Courses and Lect. 378, Springer, Vienna (1997), 291-348.
- [33] M. Matar, Controllability of fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions, Int. J. Math. Anal. (Ruse) 4 (2010), no. 21-24, 1105-1116.
- [34] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.
- [35] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), no. 5, 985-999.
- [36] M. Muslim and R. P. Agarwal, Exact controllability of an integro-differential equation with deviated argument, Funct. Differ. Equ. 21 (2014), no. 1-2, 31-45.
- [37] D. O’Regan and R. Precup, Existence criteria for integral equations in Banach spaces, J. Inequal. Appl. 6 (2001), no. 1, 77-97.
- [38] P. Ostalczyk, D. Sankowski and J. Nowakowski, Non-integer Order Calculus and its Applications, Lect. Notes Electr. Eng. 496, Springer, Cham, 2019.
- [39] I. Podlubny, Fractional Differential Equations, Math. Sci. Eng. 198, Academic Press, San Diego, 1999.
- [40] M. D. Quinn and N. Carmichael, An approach to nonlinear control problems using fixed-point methods, degree theory and pseudo-inverses, Numer. Funct. Anal. Optim. 7 (1984/85), no. 2-3, 197-219.
- [41] V. Singh, Controllability of Hilfer fractional differential systems with non-dense domain, Numer. Funct. Anal. Optim. 40 (2019), no. 13, 1572-1592.
- [42] V. Singh and D. N. Pandey, Controllability of fractional impulsive quasilinear differential systems with state dependent delay, Int. J. Dyn. Control 7 (2019), no. 1, 313-325.
- [43] J. Wang, W. Wei and Y. Yang, Fractional nonlocal integrodifferential equations and its optimal control in Banach spaces, J. Korean Soc. Ind. Appl. Math. 14 (2010), no. 2, 79-91.
- [44] J. Wang and Y. Zhou, Existence and controllability results for fractional semilinear differential inclusions, Nonlinear Anal. Real World Appl. 12 (2011), no. 6, 3642-3653.
- [45] J. Wang and Y. Zhou, Complete controllability of fractional evolution systems, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), no. 11, 4346-4355.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-1c89d103-0a22-486b-8ef3-806e0b101ab1