Yıl: 2017 Cilt: 41 Sayı: 4 Sayfa Aralığı: 1042 - 1052 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Terminal value problem for causal differential equations with a Caputo fractional derivative

Öz:
In this paper, we have given new definitions and obtained the unique solution of a fractional causal terminal value problem by combining the technique of generalized quasilinearization in the sense of upper and lower solutions.
Anahtar Kelime:

Konular: Matematik
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Aftabizadeh AR, Lakshmikantham V. On the theory of terminal value problems for ordinary differential equations. Nonlinear Anal-Theor 1981; 11: 1173-1180.
  • [2] Agarwal RP, Zhou Y, Wang JR, Luo X. Fractional functional differential equations with causal operators in Banach spaces. Math Comput Model 2011; 54: 1440-1452.
  • [3] Ahmad B, Khan RA. Generalized quasilinearization method for nonlinear terminal value problems. Southeast Asian Bull Math 2004; 27: 953-958.
  • [4] Baleanu D, Mustafa OG, O’Regan D. Kamenev-type oscillation result for a linear (1 +alpha )–order fractional differential equation. Appl Math Comput 2015; 259: 374-378.
  • [5] Baleanu D, Rezapour S, Salehi S. On the existence of solutions for a fractional finite difference inclusion via three points boundary conditions. Adv Differ Equ-ny 2015; 2015: 242.
  • [6] Bellman R. Methods of Nonlinear Analysis. New York, NY, USA: Academic Press, 1973.
  • [7] Bellman R, Kalaba R. Quasilinearization and Nonlinear Boundary Value Problems. New York, NY, USA: American Elsevier Publishing Company, 1965.
  • [8] Corduneanu C. Functional equations with causal operators, Stab and Contr. New York, NY, USA: Taylor & Francis, 2005.
  • [9] Dhage BC. Strict and non-strict inequalities for implicit first order causal differential equations. Electron J Qual Theo 2011; 91: 1-6.
  • [10] Drici Z, Vasundhara DJ, McRae FA. On the comparison principle and existence results for terminal value problems. Nonlinear Studies 2014; 21: 269-282.
  • [11] K¨oksal S, Yakar C. Generalized quasilinearization method with initial time difference. Simulation an International Journal of Electrical, Electronic and other Physical Systems 2002; 24: 5.
  • [12] Ladde GS, Lakshmikantham V, Vatsala AS. Monotone iterative techniques for nonlinear differential equations. London, England: Pitman, 1985.
  • [13] Lakshmikantham V, Leela S, Drici Z, McRae FA. Theory of causal differential equations. Paris, France: Atlantis Press, 2009.
  • [14] Lakshmikantham V, Leela S, McRae FA. Improved generalized quasilinearization (GQL) method. Nonlinear Analysis 1995; 24: 1627-1637.
  • [15] Lakshmikantham V, Shahzad N. Further generalization of generalized quasilinearization method. Journal of Applied Mathematics and Stochastic Analysis 1994; 7: 545-552.
  • [16] Lakshmikantham V, Vasundhara DJ. Theory of Fractional Differential Equations in a Banach Space. European Journal of Pure and Applied Mathematics 2008; 1: 38-45.
  • [17] Lakshmikantham V, Vatsala AS. Generalized Quasilinearization for Nonlinear Problems. Dordrecht, Holland: Kluwer Academic Publishers, 1998.
  • [18] Lakshmikantham V, Vatsala AS. Theory of fractional differential inequalities and applications. Communications in Applied Analysis 2007; 11: 395-402.
  • [19] Lupulescu V. Functional differential equations with causal operators. International Journal of Nonlinear Science 2011; 11: 499-505.
  • [20] McNabb A, Weir G. Comparison theorems for causal functional differential equations. P Am Math Soc 1988; 104: 449-452.
  • [21] McRae FA, Drici Z, Vasundhara DJ. Terminal Value Problems for Caputo Fractional Differential Equations. Dyn Syst Appl 2013; 22.
  • [22] Ramirez JD, Vatsala AS. Monotone iterative technique for fractional differential equations with periodic boundary conditions. Opuscula Mathematica 2009; 29: 289-304.
  • [23] Shishuo Q. Extremal solutions of terminal value problems for nonlinear impulsive integro-differential equations in Banach spaces. Appl Math Ser B 2000; 15: 37-44.
  • [24] Vasundhara DJ. On Existence of Solution of an Impulsive Terminal Value Problem. Elektronnoe Modelirovanie 2003; 25: 115-121.
  • [25] Vasundhara DJ, Suseela C. Quasilinearization for fractional differential equations. Communications in Applied Analysis 2008; 12: 407-418.
  • [26] Yakar C. Quasilinearization Method in Causal Differential Equations with Initial Time Difference. Commun Fac Sci Univ Ank Series A1 2014; 63: 55-71.
  • [27] Yakar C, Yakar A. A refinement of quasilinearization method for Caputo sense fractional order differential equations. Abstract and Applied Analysis 2010; 10.
  • [28] Yakar C, Yakar A. Further generalization of quasilinearization method with initial time difference. Journal of Applied Functional Analysis 2009; 4: 714-727.
APA YAKAR C, Arslan M (2017). Terminal value problem for causal differential equations with a Caputo fractional derivative. , 1042 - 1052.
Chicago YAKAR COSKUN,Arslan Mehmet Terminal value problem for causal differential equations with a Caputo fractional derivative. (2017): 1042 - 1052.
MLA YAKAR COSKUN,Arslan Mehmet Terminal value problem for causal differential equations with a Caputo fractional derivative. , 2017, ss.1042 - 1052.
AMA YAKAR C,Arslan M Terminal value problem for causal differential equations with a Caputo fractional derivative. . 2017; 1042 - 1052.
Vancouver YAKAR C,Arslan M Terminal value problem for causal differential equations with a Caputo fractional derivative. . 2017; 1042 - 1052.
IEEE YAKAR C,Arslan M "Terminal value problem for causal differential equations with a Caputo fractional derivative." , ss.1042 - 1052, 2017.
ISNAD YAKAR, COSKUN - Arslan, Mehmet. "Terminal value problem for causal differential equations with a Caputo fractional derivative". (2017), 1042-1052.
APA YAKAR C, Arslan M (2017). Terminal value problem for causal differential equations with a Caputo fractional derivative. Turkish Journal of Mathematics, 41(4), 1042 - 1052.
Chicago YAKAR COSKUN,Arslan Mehmet Terminal value problem for causal differential equations with a Caputo fractional derivative. Turkish Journal of Mathematics 41, no.4 (2017): 1042 - 1052.
MLA YAKAR COSKUN,Arslan Mehmet Terminal value problem for causal differential equations with a Caputo fractional derivative. Turkish Journal of Mathematics, vol.41, no.4, 2017, ss.1042 - 1052.
AMA YAKAR C,Arslan M Terminal value problem for causal differential equations with a Caputo fractional derivative. Turkish Journal of Mathematics. 2017; 41(4): 1042 - 1052.
Vancouver YAKAR C,Arslan M Terminal value problem for causal differential equations with a Caputo fractional derivative. Turkish Journal of Mathematics. 2017; 41(4): 1042 - 1052.
IEEE YAKAR C,Arslan M "Terminal value problem for causal differential equations with a Caputo fractional derivative." Turkish Journal of Mathematics, 41, ss.1042 - 1052, 2017.
ISNAD YAKAR, COSKUN - Arslan, Mehmet. "Terminal value problem for causal differential equations with a Caputo fractional derivative". Turkish Journal of Mathematics 41/4 (2017), 1042-1052.