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Terminal value problems with causal operators

Yıl 2018, Cilt: 47 Sayı: 4, 897 - 907, 01.08.2018

Öz

The well-known techniques of monotone iterative have been investigated and expanded for the causal terminal value problem (CTVP). This method construct the monotone sequences of the solutions of linear CTVPs by using the upper and lower solutions. Moreover, these sequence of functions are uniformly and monotonically converge to the extremal solutions of the CTVP.

Kaynakça

  • Aftabizadeh, A.R. and Lakshmikantham, V. On the theory of terminal value problems for ordinary differential equations, Nonlinear Analysis, 5(11), 11731180, 1981.
  • Agarwal, R.P., Zhou, Y., Wang, J.R. and Luo, X. Fractional functional differential equations with causal operators in Banach spaces, Mathematical and Computer Modelling, 54, 1440 1452, 2011.
  • Corduneanu, C. Functional equations with causal operators, stability and control: The- ory,Methods and Applications, New York, NY, USA: Taylor & Francis, 2005.
  • Devi, J.V. Generalized monotone iterative technique for set differential equations involving causal operators with memory, Int. J. Adv. Eng. Sci. Appl. Math., 3(1-4), 74-84, 2011.
  • Dhage, B. C. Strict and non-strict inequalities for implicit first order causal differential equations, Electronic Journal of Qualitative Theory of Dierential Equations, 91, 1-6, 2011.
  • Domingues, J. S. Gompertz Model: Resolution and analysis for tumors, Journal of Mathematical Modelling and Application, 1(7), 70-77, 2012.
  • Drici, Z., McRae, F.A. and Devi, J.V. Differential equations with causal operators in a Banach space, Nonlinear Anal. 62, 301313, 2005.
  • Drici, Z., Devi, J.V. and McRae, F.A. On the comparison principle and existence results for terminal value problems, Nonlinear Studies, 21, 269-282, 2014.
  • Ladde, G.S. and Lakshmikantham, V. and Vatsala, A.S. Monotone iterative techniques for nonlinear differential equations, London, England, Pitman, 1985.
  • Lakshmikantham, V. and Leela, S. Differential and Integral Inequalities: Ordinary differ- ential equations, New York, London, Academic Press, 1969.
  • Lakshmikantham, V., Leela, S., Drici, Z. and McRae, F.A. Theory of causal differential equations, Amsterdam - Paris: Atlantis Press, 2009.
  • Lupulescu, V. Functional differential equations with causal operators, International Journal of Nonlinear Science, 11(4), 499-505, 2011.
  • McNabb, A. and Weir, G. Comparison theorems for causal functional differential equations, Proc. AMS 104, 449-452, 1998.
  • McRae, F.A. Monotone iterative technique and existence results for fractional differential Equations, Nonlinear Analysis: Theory, Methods and Applications 71 (12), 60936096, 2009.
  • McRae, F.A., Drici, Z. and Devi, J.V. Terminal Value Problems for Caputo Fractional Differential Equations, Dynamic Systems and Applications, 22, 2013.
  • Nieto, J. J. , Jiang, Y. and Jurang, Y. Monotone iterative method for functional differential equations, Nonlinear Anal., 32, 741747, 1998.
  • Nieto, J. J. and Rodriguez-Lopez, R. Monotone method for first-order functional differential equations, Comput. Math. Appl., 52, 471484, 2006.
  • Shishuo, Q. Extremal solutions of terminal value problems for nonlinear impulsive integro- differential equations in Banach spaces, Applied Mathematics-A Journal of Chinese Universities, 15(1), 37-44, 2000.
  • Yakar, C. Initial Time Difference Quasilinearization Method in Causal Differential Equation with Initial Time Difference, Communications in Mathematics and Statistics, Faculty of Sciences Ankara University, 63, 3-12, 2014.
  • Yakar, C., Arslan, I., Çiçek, M. Monotone Iterative Technique by Upper and Lower Solutions with Initial Time Difference, Miskolc Mathematical Notes, 16(1), 575-586, 2015.
  • Yakar, C., Bal, B. and Yakar, A. Monotone technique in terms of two monotone functions in finite systems, Journal of Concrete and Applicable Mathematics, 9(3), 233-239, 2011.
  • Yakar, C. and Gücen, M. B. Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals, Journal of Applied Mathematics, doi:10.1155/2014/832015, 2014.
  • Wang, W. and Tian, J. Generalized monotone iterative method for nonlinear boundary value problems with causal operators, Boundary Value Problems, 2014:192, 2014.
  • Yakar, C. and Arslan, M. Terminal value problem for causal differential equations with a Caputo fractional derivative, Turkish Journal of Mathematics, 41, 1042-1052, 2017.
Yıl 2018, Cilt: 47 Sayı: 4, 897 - 907, 01.08.2018

Öz

Kaynakça

  • Aftabizadeh, A.R. and Lakshmikantham, V. On the theory of terminal value problems for ordinary differential equations, Nonlinear Analysis, 5(11), 11731180, 1981.
  • Agarwal, R.P., Zhou, Y., Wang, J.R. and Luo, X. Fractional functional differential equations with causal operators in Banach spaces, Mathematical and Computer Modelling, 54, 1440 1452, 2011.
  • Corduneanu, C. Functional equations with causal operators, stability and control: The- ory,Methods and Applications, New York, NY, USA: Taylor & Francis, 2005.
  • Devi, J.V. Generalized monotone iterative technique for set differential equations involving causal operators with memory, Int. J. Adv. Eng. Sci. Appl. Math., 3(1-4), 74-84, 2011.
  • Dhage, B. C. Strict and non-strict inequalities for implicit first order causal differential equations, Electronic Journal of Qualitative Theory of Dierential Equations, 91, 1-6, 2011.
  • Domingues, J. S. Gompertz Model: Resolution and analysis for tumors, Journal of Mathematical Modelling and Application, 1(7), 70-77, 2012.
  • Drici, Z., McRae, F.A. and Devi, J.V. Differential equations with causal operators in a Banach space, Nonlinear Anal. 62, 301313, 2005.
  • Drici, Z., Devi, J.V. and McRae, F.A. On the comparison principle and existence results for terminal value problems, Nonlinear Studies, 21, 269-282, 2014.
  • Ladde, G.S. and Lakshmikantham, V. and Vatsala, A.S. Monotone iterative techniques for nonlinear differential equations, London, England, Pitman, 1985.
  • Lakshmikantham, V. and Leela, S. Differential and Integral Inequalities: Ordinary differ- ential equations, New York, London, Academic Press, 1969.
  • Lakshmikantham, V., Leela, S., Drici, Z. and McRae, F.A. Theory of causal differential equations, Amsterdam - Paris: Atlantis Press, 2009.
  • Lupulescu, V. Functional differential equations with causal operators, International Journal of Nonlinear Science, 11(4), 499-505, 2011.
  • McNabb, A. and Weir, G. Comparison theorems for causal functional differential equations, Proc. AMS 104, 449-452, 1998.
  • McRae, F.A. Monotone iterative technique and existence results for fractional differential Equations, Nonlinear Analysis: Theory, Methods and Applications 71 (12), 60936096, 2009.
  • McRae, F.A., Drici, Z. and Devi, J.V. Terminal Value Problems for Caputo Fractional Differential Equations, Dynamic Systems and Applications, 22, 2013.
  • Nieto, J. J. , Jiang, Y. and Jurang, Y. Monotone iterative method for functional differential equations, Nonlinear Anal., 32, 741747, 1998.
  • Nieto, J. J. and Rodriguez-Lopez, R. Monotone method for first-order functional differential equations, Comput. Math. Appl., 52, 471484, 2006.
  • Shishuo, Q. Extremal solutions of terminal value problems for nonlinear impulsive integro- differential equations in Banach spaces, Applied Mathematics-A Journal of Chinese Universities, 15(1), 37-44, 2000.
  • Yakar, C. Initial Time Difference Quasilinearization Method in Causal Differential Equation with Initial Time Difference, Communications in Mathematics and Statistics, Faculty of Sciences Ankara University, 63, 3-12, 2014.
  • Yakar, C., Arslan, I., Çiçek, M. Monotone Iterative Technique by Upper and Lower Solutions with Initial Time Difference, Miskolc Mathematical Notes, 16(1), 575-586, 2015.
  • Yakar, C., Bal, B. and Yakar, A. Monotone technique in terms of two monotone functions in finite systems, Journal of Concrete and Applicable Mathematics, 9(3), 233-239, 2011.
  • Yakar, C. and Gücen, M. B. Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals, Journal of Applied Mathematics, doi:10.1155/2014/832015, 2014.
  • Wang, W. and Tian, J. Generalized monotone iterative method for nonlinear boundary value problems with causal operators, Boundary Value Problems, 2014:192, 2014.
  • Yakar, C. and Arslan, M. Terminal value problem for causal differential equations with a Caputo fractional derivative, Turkish Journal of Mathematics, 41, 1042-1052, 2017.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Coşkun Yakar

Mehmet Arslan

Yayımlanma Tarihi 1 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 47 Sayı: 4

Kaynak Göster

APA Yakar, C., & Arslan, M. (2018). Terminal value problems with causal operators. Hacettepe Journal of Mathematics and Statistics, 47(4), 897-907.
AMA Yakar C, Arslan M. Terminal value problems with causal operators. Hacettepe Journal of Mathematics and Statistics. Ağustos 2018;47(4):897-907.
Chicago Yakar, Coşkun, ve Mehmet Arslan. “Terminal Value Problems With Causal Operators”. Hacettepe Journal of Mathematics and Statistics 47, sy. 4 (Ağustos 2018): 897-907.
EndNote Yakar C, Arslan M (01 Ağustos 2018) Terminal value problems with causal operators. Hacettepe Journal of Mathematics and Statistics 47 4 897–907.
IEEE C. Yakar ve M. Arslan, “Terminal value problems with causal operators”, Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 4, ss. 897–907, 2018.
ISNAD Yakar, Coşkun - Arslan, Mehmet. “Terminal Value Problems With Causal Operators”. Hacettepe Journal of Mathematics and Statistics 47/4 (Ağustos 2018), 897-907.
JAMA Yakar C, Arslan M. Terminal value problems with causal operators. Hacettepe Journal of Mathematics and Statistics. 2018;47:897–907.
MLA Yakar, Coşkun ve Mehmet Arslan. “Terminal Value Problems With Causal Operators”. Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 4, 2018, ss. 897-0.
Vancouver Yakar C, Arslan M. Terminal value problems with causal operators. Hacettepe Journal of Mathematics and Statistics. 2018;47(4):897-90.