Araştırma Makalesi
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Yıl 2019, Cilt: 68 Sayı: 1, 1206 - 1228, 01.02.2019

M. Tamilselvan

https://doi.org/10.31801/cfsuasmas.513695

Öz

Kaynakça

  • Abada, N., Benchohra, M. and Hammouche, H., Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions, Journal of Differential Equations, 246(10) (2009), 3834-3863.
  • Aizicovici, S. and McKibben, M., Existence results for a class of abstract nonlocal Cauchy problems, Nonlinear Analysis, 39 (2000), 649-668.
  • Bainov, D.D. and Simeonov, P.S., Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical Group, England, 1993.
  • Benchohra, M. Henderson J. and Ntouyas, S.K. Impulsive Differential Equations and Inclusions, Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, 2006.
  • Bohnenblust, H.F. and Karlin, S., On a Theorem of Ville, in: Contributions to the Theory of Games, vol. I, Princeton University Press, Princeton, NJ, 155-160, 1950.
  • Byszewski, L., Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, Journal of Mathematical Analysis and Applications, 162 (1991), 494-505.
  • Byszewski L. and Akca, H. On a mild solution of a semilinear functional-differential evolution nonlocal problem, Journal of Applied Mathematics and Stochastic Analysis, 10(3) (1997), 265-271.
  • Byszewski, L. and Lakshmikantham, V., Theorem about the existence and uniqueness of solutions of a nonlocal Cauchy problem in a Banach space, Applicable Analysis, 40 (1990), 11-19.
  • Chang, Y. and Nieto, J.J., Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators, Numerical Functional Analysis and Optimization, 30 (2009), 227-244.
  • Chang, Y.-K. and Chalishajar, D.N., Controllability of mixed Volterra-Fredholm type integrodifferential inclusions in Banach spaces, Journal of Franklin Institute, 345 (2008), 499-507.
  • Chang, J. and Liu, H., Existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α-norm, Nonlinear Analysis, 71 (2009), 3759-3768.
  • Dauer, J.P., Mahmudov N.I. and Matar, M.M., Approximate controllability of backward stochastic evolution equations in Hilbert spaces, Journal of Mathematical Analysis and Application, 323(1) (2006), 42-56.
  • Deimling, K., Multivalued Differential Equations, De Gruyter, Berlin, 1992.
  • Ezzinbi, K., Fu X. and Hilal, K., Existence and regularity in the α -norm for some neutral partial differential equations with nonlocal conditions, Nonlinear Analysis, 67 (2007), 1613-1622.
  • Ezzinbi L. and Ghnimi, S. Existence and regularity of solutions for neutral partial functional integro-differential equations, Nonlinear Analysis: Real World Applications, 11 (2010), 2335-2344.
  • Fu, X. and Ezzinbi, K., Existence of solutions for neutral functional differential evolution equations with nonlocal conditions, Nonlinear Analysis, 54 (2003), 215-227.
  • Fu, X. Gao, Y. and Zhang, Y., Existence of solutions for neutral integrodifferential equations with nonlocal conditions, Taiwanese Journal of Mathematics, 16(5) (2012), 1879-1909.
  • Guendouzi, T. and Bousmaha, L., Approximate controllability of fractional neutral stochastic functional integro-differential inclusions with infinite delay, Qualitative Theory of Dynamical System, 13 (2014), 89-119.
  • Grimmer, R., Reslvent operator for integral equations in a Banach space, Transactions of American Mathematical Soceity, 273 (1982), 333-349.
  • Grimmer, R. and Kappel, F., Series expansions for resolvents of volterra integro-differential equations on Banach spaces, SIAM Journal on Mathematical Analysis, 15 (1984), 595-604.
  • Grimmer, R. and Pritchard, A. J., Analytic resolvent operators for integral equations in a Banach space, Journal of Differential Equations, 50 (1983), 234-259.
  • Henríquez, H.R., Approximate controllability of linear distributed control systems, Applied Mathematical Letters, 21(10) (2008), 1041-1045.
  • Kumar, R., Nonlocal cauchy problem for analytic rsolvent integrodifferential equations in Banach spaces, Applied Mathematics and Computation, 204 (2008), 352-362.
  • Laksmikantham, V., Bainov D. and Simenov, P. S., Theory of impulsive differential equations, Series in Modern Applied Mathematics, 6. World Scientific Publishing Co., Inc., Teaneck, NJ, 1989.
  • Lasota, A. and Opial, Z., An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations or noncompact acyclic-valued map, Bulletin L'Academic Polonaise des Science, Serie des Sciences Mathematiques, Astronomiques et Physiques, 13 (1965), 781-786.
  • Liu Z. and Lv, J., Approximate controllability of fractional functional evolution inclusions with delay in Hilbert spaces, IMA Journal of Mathematical Control and Information, 31 (2013), 363-383.
  • Liu, J., Commutativity of resolvent operator in integro-differential equations, Volterra Equations and Applications Arlington, Tx, 1996, 309-316.
  • Miller, B.M. and Rubinovich, E.Y., Impulsive Control in Continuous and Discrete-Continuous Systems, Kluwer Academic/Plenum Publishers, New York, 2003.
  • Mahmudov, N.I. and Denker, A., On controllability of linear stochastic systems, International Journal of Control, 73 (2000), 144-151.
  • Mahmudov, N.I., Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Analysis: Theory, Methods and Applications, 68(3) (2008), 536-546.
  • Mahmudov N.I., and Zorlu, S., On the approximate controllability of fractional evolution equations with compact analytic semigroup, Journal of Computational and Applied Mathematics, 259 (2014), 194-204.
  • Mahmudov, N.I., Approximate controllability of some nonlinear systems in Banach spaces, Boundary value Problems, 2013(1) (2013), 1-13.
  • Mokkedem, F.Z. and Fu, X., Approximate controllability of semilinear neutral integrodifferential systems with finite delay, Applied Mathematics and Computation, 242 (2014), 202-215.
  • Pazy, A., Semigroups of Linear operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
  • Sakthivel, R., Ganesh R. and Anthoni, S.M., Approximate controllability of fractional nonlinear differential inclusions, Applied Mathematics and Computation, 225 (2013), 708-717.
  • Sakthivel, R., Mahmudov N.I. and Kim, J.H., Approximate controllability of nonlinear impulsive differential systems, Reports on Mathematical Physics, 60(1) (2007), 85-96. Hu S. and Papageorgiou, N.S., Handbook of Multivalued Analysis (Theory), Kluwer Academic Publishers, Dordrecht Boston, London, 1997.
  • Vijayakumar, V., Ravichandran C. and Murugesu, R., Approximate controllability for a class of fractional neutral integro-differential inclusions with state-dependent delay, Nonlinear studies, 20(4) (2013), 511-530.
  • Vijayakumar, V., Selvakumar A. and Murugesu, R., Controllability for a class of fractional neutral integro-differential equations with unbounded delay, Applied Mathematics and Computation, 232 (2014), 303-312.
  • Vijayakumar, V., Ravichandran C., Murugesu R. and Trujillo, J.J., Controllability results for a class of fractional semilinear integro-differential inclusions via resolvent operators, Applied Mathematics and Computation, 247 (2014), 152-161.

Approximate controllability of neutral integrodifferential inclusions via resolvent operators

Yıl 2019, Cilt: 68 Sayı: 1, 1206 - 1228, 01.02.2019

M. Tamilselvan

https://doi.org/10.31801/cfsuasmas.513695

Öz

In this work, a set of sufficient conditions are established for the approximate controllability for neutral integrodifferential inclusions in Banach spaces. The theory of fractional power and α-norm is used because of the spatial derivatives in the nonlinear term of the system. Bohnenblust-Karlin's fixed point theorem is used to prove our main results. Further, this result is extended to study the approximate controllability for nonlinear functional control system with nonlocal conditions. An example is also given to illustrate our main results.

Anahtar Kelimeler

Approximate controllability integrodifferential inclusions analytic semigroup resolvent operator nonlocal conditions

Kaynakça

  • Abada, N., Benchohra, M. and Hammouche, H., Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions, Journal of Differential Equations, 246(10) (2009), 3834-3863.
  • Aizicovici, S. and McKibben, M., Existence results for a class of abstract nonlocal Cauchy problems, Nonlinear Analysis, 39 (2000), 649-668.
  • Bainov, D.D. and Simeonov, P.S., Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical Group, England, 1993.
  • Benchohra, M. Henderson J. and Ntouyas, S.K. Impulsive Differential Equations and Inclusions, Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, 2006.
  • Bohnenblust, H.F. and Karlin, S., On a Theorem of Ville, in: Contributions to the Theory of Games, vol. I, Princeton University Press, Princeton, NJ, 155-160, 1950.
  • Byszewski, L., Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, Journal of Mathematical Analysis and Applications, 162 (1991), 494-505.
  • Byszewski L. and Akca, H. On a mild solution of a semilinear functional-differential evolution nonlocal problem, Journal of Applied Mathematics and Stochastic Analysis, 10(3) (1997), 265-271.
  • Byszewski, L. and Lakshmikantham, V., Theorem about the existence and uniqueness of solutions of a nonlocal Cauchy problem in a Banach space, Applicable Analysis, 40 (1990), 11-19.
  • Chang, Y. and Nieto, J.J., Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators, Numerical Functional Analysis and Optimization, 30 (2009), 227-244.
  • Chang, Y.-K. and Chalishajar, D.N., Controllability of mixed Volterra-Fredholm type integrodifferential inclusions in Banach spaces, Journal of Franklin Institute, 345 (2008), 499-507.
  • Chang, J. and Liu, H., Existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α-norm, Nonlinear Analysis, 71 (2009), 3759-3768.
  • Dauer, J.P., Mahmudov N.I. and Matar, M.M., Approximate controllability of backward stochastic evolution equations in Hilbert spaces, Journal of Mathematical Analysis and Application, 323(1) (2006), 42-56.
  • Deimling, K., Multivalued Differential Equations, De Gruyter, Berlin, 1992.
  • Ezzinbi, K., Fu X. and Hilal, K., Existence and regularity in the α -norm for some neutral partial differential equations with nonlocal conditions, Nonlinear Analysis, 67 (2007), 1613-1622.
  • Ezzinbi L. and Ghnimi, S. Existence and regularity of solutions for neutral partial functional integro-differential equations, Nonlinear Analysis: Real World Applications, 11 (2010), 2335-2344.
  • Fu, X. and Ezzinbi, K., Existence of solutions for neutral functional differential evolution equations with nonlocal conditions, Nonlinear Analysis, 54 (2003), 215-227.
  • Fu, X. Gao, Y. and Zhang, Y., Existence of solutions for neutral integrodifferential equations with nonlocal conditions, Taiwanese Journal of Mathematics, 16(5) (2012), 1879-1909.
  • Guendouzi, T. and Bousmaha, L., Approximate controllability of fractional neutral stochastic functional integro-differential inclusions with infinite delay, Qualitative Theory of Dynamical System, 13 (2014), 89-119.
  • Grimmer, R., Reslvent operator for integral equations in a Banach space, Transactions of American Mathematical Soceity, 273 (1982), 333-349.
  • Grimmer, R. and Kappel, F., Series expansions for resolvents of volterra integro-differential equations on Banach spaces, SIAM Journal on Mathematical Analysis, 15 (1984), 595-604.
  • Grimmer, R. and Pritchard, A. J., Analytic resolvent operators for integral equations in a Banach space, Journal of Differential Equations, 50 (1983), 234-259.
  • Henríquez, H.R., Approximate controllability of linear distributed control systems, Applied Mathematical Letters, 21(10) (2008), 1041-1045.
  • Kumar, R., Nonlocal cauchy problem for analytic rsolvent integrodifferential equations in Banach spaces, Applied Mathematics and Computation, 204 (2008), 352-362.
  • Laksmikantham, V., Bainov D. and Simenov, P. S., Theory of impulsive differential equations, Series in Modern Applied Mathematics, 6. World Scientific Publishing Co., Inc., Teaneck, NJ, 1989.
  • Lasota, A. and Opial, Z., An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations or noncompact acyclic-valued map, Bulletin L'Academic Polonaise des Science, Serie des Sciences Mathematiques, Astronomiques et Physiques, 13 (1965), 781-786.
  • Liu Z. and Lv, J., Approximate controllability of fractional functional evolution inclusions with delay in Hilbert spaces, IMA Journal of Mathematical Control and Information, 31 (2013), 363-383.
  • Liu, J., Commutativity of resolvent operator in integro-differential equations, Volterra Equations and Applications Arlington, Tx, 1996, 309-316.
  • Miller, B.M. and Rubinovich, E.Y., Impulsive Control in Continuous and Discrete-Continuous Systems, Kluwer Academic/Plenum Publishers, New York, 2003.
  • Mahmudov, N.I. and Denker, A., On controllability of linear stochastic systems, International Journal of Control, 73 (2000), 144-151.
  • Mahmudov, N.I., Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Analysis: Theory, Methods and Applications, 68(3) (2008), 536-546.
  • Mahmudov N.I., and Zorlu, S., On the approximate controllability of fractional evolution equations with compact analytic semigroup, Journal of Computational and Applied Mathematics, 259 (2014), 194-204.
  • Mahmudov, N.I., Approximate controllability of some nonlinear systems in Banach spaces, Boundary value Problems, 2013(1) (2013), 1-13.
  • Mokkedem, F.Z. and Fu, X., Approximate controllability of semilinear neutral integrodifferential systems with finite delay, Applied Mathematics and Computation, 242 (2014), 202-215.
  • Pazy, A., Semigroups of Linear operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
  • Sakthivel, R., Ganesh R. and Anthoni, S.M., Approximate controllability of fractional nonlinear differential inclusions, Applied Mathematics and Computation, 225 (2013), 708-717.
  • Sakthivel, R., Mahmudov N.I. and Kim, J.H., Approximate controllability of nonlinear impulsive differential systems, Reports on Mathematical Physics, 60(1) (2007), 85-96. Hu S. and Papageorgiou, N.S., Handbook of Multivalued Analysis (Theory), Kluwer Academic Publishers, Dordrecht Boston, London, 1997.
  • Vijayakumar, V., Ravichandran C. and Murugesu, R., Approximate controllability for a class of fractional neutral integro-differential inclusions with state-dependent delay, Nonlinear studies, 20(4) (2013), 511-530.
  • Vijayakumar, V., Selvakumar A. and Murugesu, R., Controllability for a class of fractional neutral integro-differential equations with unbounded delay, Applied Mathematics and Computation, 232 (2014), 303-312.
  • Vijayakumar, V., Ravichandran C., Murugesu R. and Trujillo, J.J., Controllability results for a class of fractional semilinear integro-differential inclusions via resolvent operators, Applied Mathematics and Computation, 247 (2014), 152-161.
Toplam 39 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

M. Tamilselvan 0000-0001-7043-1103

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 14 Şubat 2018
Kabul Tarihi 26 Mayıs 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA Tamilselvan, M. (2019). Approximate controllability of neutral integrodifferential inclusions via resolvent operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 1206-1228. https://doi.org/10.31801/cfsuasmas.513695
AMA Tamilselvan M. Approximate controllability of neutral integrodifferential inclusions via resolvent operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):1206-1228. doi:10.31801/cfsuasmas.513695
Chicago Tamilselvan, M. “Approximate Controllability of Neutral Integrodifferential Inclusions via Resolvent Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 1206-28. https://doi.org/10.31801/cfsuasmas.513695.
EndNote Tamilselvan M (01 Şubat 2019) Approximate controllability of neutral integrodifferential inclusions via resolvent operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 1206–1228.
IEEE M. Tamilselvan, “Approximate controllability of neutral integrodifferential inclusions via resolvent operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 1206–1228, 2019, doi: 10.31801/cfsuasmas.513695.
ISNAD Tamilselvan, M. “Approximate Controllability of Neutral Integrodifferential Inclusions via Resolvent Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 1206-1228. https://doi.org/10.31801/cfsuasmas.513695.
JAMA Tamilselvan M. Approximate controllability of neutral integrodifferential inclusions via resolvent operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1206–1228.
MLA Tamilselvan, M. “Approximate Controllability of Neutral Integrodifferential Inclusions via Resolvent Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 1206-28, doi:10.31801/cfsuasmas.513695.
Vancouver Tamilselvan M. Approximate controllability of neutral integrodifferential inclusions via resolvent operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):1206-28.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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