Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 9 Sayı: 1, 176 - 182, 28.04.2021

Öz

Kaynakça

  • [1] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, North-Holland mathematics studies, 204. Elsevier Science B.V, Amsterdam, 2006.
  • [2] I. J. Cabrera and J. Rocha and K.B. Sadarangani, Lyapunov type inequalities for a fractional thermostat model, RACSAM Rev. R. Acad. A. Vol:112, No.1 (2018), 17-24.
  • [3] J. J. Nieto and J. Pimentel, Positive solutions of a fractional thermostat model, Bound. Value Probl. Vol: 2013, No.1 (2013), 1-11.
  • [4] Y. Z. Chen, Krasnoselskii-type fixed point theorems using a-concave operators, J. Fix. Point Theory A. Vol:22, No.3 (2020), 1-8.
  • [5] C. Shen and H. Zhou and L. Yang, Existence of positive solutions of a nonlinear differential equation for a thermostat model, Math. Methods Appl. Sci. Vol:41, No.16 (2018), 6145-6154.
  • [6] C. F. Li and X. N. Luo and Y. Zhou, Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Comput. Math. Appl. Vol:59, No.3 (2010), 1363-1375.
  • [7] B. Lo´pez and J. Rocha and K. Sadarangani, Positive solutions in the space of Ho¨lder functions to a fractional thermostat model, RACSAM Rev. R. Acad. A. Vol:113, (2019), 2449-2460.
  • [8] C. Shen and H. Zhou and L. Yang, Existence and nonexistence of positive solutions of a fractional thermostat model with a parameter, Math. Methods Appl. Sci. Vol:39, No.15 (2016), 4504-4511.
  • [9] M. Jleli and B. Samet, Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions, Math. Inequal. Appl. Vol:18, No.2 (2015), 443-451.
  • [10] D. O’Regan and B. Samet, Lyapunov-type inequalities for a class of fractional differential equations, J. Inequal. Appl. Vol:2015, No.1 (2015), 1-10.
  • [11] A.C. Thompson, On certain contraction mappings in a partially ordered vector space, Proc. Am. Math.Soc. Vol:14, No.3 (1963), 438-443.
  • [12] Y. He, Existence and multiplicity of positive solutions for singular fractional differential equations with integral boundary value conditions, Adv. Differ. Equ. Vol:2016, No.1 (2016), 1-14.
  • [13] M. Jiang and S. Zhong, Successively iterative method for fractional differential equations with integral boundary conditions, Appl. Math. Lett. Vol:38, (2014), 94-99.
  • [14] C.M. Su and J.P. Sun and Y.H. Zhao, Existence and uniqueness of solutions for BVP of nonlinear fractional differential equation, Int. J. Differ. Eq. Vol:2017, (2017), 1-7.
  • [15] C. Yang and C.B. Zhai, Uniqueness of positive solutions for a fractional differential equation via a fixed point theorem of a sum operator, Electron. J. Differ. Eq. Vol:2012, No.70 (2012), 808-826.
  • [16] J.R. Yue and J.P. Sun and S. Zhang, Existence of positive solution for BVP of nonlinear fractional differential equation, Discrete Dyn. Nat. Soc. Vol:2015, (2015), 1731-1747.
  • [17] X. L. Zhang and L. Wang and Q. Sun, Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter, Appl. Math. Comput. Vol:226, No.1-2 (2014), 708-718.
  • [18] Y. Sun and M. Zhao, Positive solutions for a class of fractional differential equations with integral boundary conditions, Appl. Math. Lett. Vol:34, No.1 (2014), 17-21.
  • [19] A. Ardjouni, A. Djoudi.: Existence and uniqueness of positive solutions for first-order nonlinear Liouville Caputo fractional differential equations, Saeo Paulo J. Math. Sci. Vol:14, No.3 (2020), 381-390.
  • [20] C.B. Zhai and R.T. Jiang, Unique solutions for a new coupled system of fractional differential equations, Adv. Differ. Equ. Vol:2018, No.1 (2018), 1-12.
  • [21] Y.Q. Wang and Y.H. Wu, Existence of uniqueness and nonexistence results of positive solution for fractional differential equations integral boundary value problems, J. Funct. Space. Vol:2018, (2018), 1-7.
  • [22] H. Baghani and J. Alzabut and J. Farokhi-Ostad, et al, Existence and uniqueness of solutions for a coupled system of sequential fractional differential equations with initial conditions, J. Pseudo-Differ. Oper. Vol:11, (2020), 1-11.
  • [23] C.B. Zhai and X.L. Zhu, Unique solution for a new system of fractional differential equations. Adv. Differ. Equ. Vol:2019, No.1 (2019), 1-19.
  • [24] T. Zhu, Existence and uniqueness of positive solutions for fractional differential equations, Bound. Value. Probl. Vol:2019, No.1 (2019), 1-11.

Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods

Yıl 2021, Cilt: 9 Sayı: 1, 176 - 182, 28.04.2021

Öz

In this paper, we consider a fractional thermostat model involving Caputo fractional derivatives. Based on recent fixed point theorems of sum operators on cones, we give the existence and uniqueness of positive solutions for the model and we can construct an iterative scheme to approximate the unique solution. In the last section, we list two concrete examples to illustrate our main results.

Kaynakça

  • [1] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, North-Holland mathematics studies, 204. Elsevier Science B.V, Amsterdam, 2006.
  • [2] I. J. Cabrera and J. Rocha and K.B. Sadarangani, Lyapunov type inequalities for a fractional thermostat model, RACSAM Rev. R. Acad. A. Vol:112, No.1 (2018), 17-24.
  • [3] J. J. Nieto and J. Pimentel, Positive solutions of a fractional thermostat model, Bound. Value Probl. Vol: 2013, No.1 (2013), 1-11.
  • [4] Y. Z. Chen, Krasnoselskii-type fixed point theorems using a-concave operators, J. Fix. Point Theory A. Vol:22, No.3 (2020), 1-8.
  • [5] C. Shen and H. Zhou and L. Yang, Existence of positive solutions of a nonlinear differential equation for a thermostat model, Math. Methods Appl. Sci. Vol:41, No.16 (2018), 6145-6154.
  • [6] C. F. Li and X. N. Luo and Y. Zhou, Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Comput. Math. Appl. Vol:59, No.3 (2010), 1363-1375.
  • [7] B. Lo´pez and J. Rocha and K. Sadarangani, Positive solutions in the space of Ho¨lder functions to a fractional thermostat model, RACSAM Rev. R. Acad. A. Vol:113, (2019), 2449-2460.
  • [8] C. Shen and H. Zhou and L. Yang, Existence and nonexistence of positive solutions of a fractional thermostat model with a parameter, Math. Methods Appl. Sci. Vol:39, No.15 (2016), 4504-4511.
  • [9] M. Jleli and B. Samet, Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions, Math. Inequal. Appl. Vol:18, No.2 (2015), 443-451.
  • [10] D. O’Regan and B. Samet, Lyapunov-type inequalities for a class of fractional differential equations, J. Inequal. Appl. Vol:2015, No.1 (2015), 1-10.
  • [11] A.C. Thompson, On certain contraction mappings in a partially ordered vector space, Proc. Am. Math.Soc. Vol:14, No.3 (1963), 438-443.
  • [12] Y. He, Existence and multiplicity of positive solutions for singular fractional differential equations with integral boundary value conditions, Adv. Differ. Equ. Vol:2016, No.1 (2016), 1-14.
  • [13] M. Jiang and S. Zhong, Successively iterative method for fractional differential equations with integral boundary conditions, Appl. Math. Lett. Vol:38, (2014), 94-99.
  • [14] C.M. Su and J.P. Sun and Y.H. Zhao, Existence and uniqueness of solutions for BVP of nonlinear fractional differential equation, Int. J. Differ. Eq. Vol:2017, (2017), 1-7.
  • [15] C. Yang and C.B. Zhai, Uniqueness of positive solutions for a fractional differential equation via a fixed point theorem of a sum operator, Electron. J. Differ. Eq. Vol:2012, No.70 (2012), 808-826.
  • [16] J.R. Yue and J.P. Sun and S. Zhang, Existence of positive solution for BVP of nonlinear fractional differential equation, Discrete Dyn. Nat. Soc. Vol:2015, (2015), 1731-1747.
  • [17] X. L. Zhang and L. Wang and Q. Sun, Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter, Appl. Math. Comput. Vol:226, No.1-2 (2014), 708-718.
  • [18] Y. Sun and M. Zhao, Positive solutions for a class of fractional differential equations with integral boundary conditions, Appl. Math. Lett. Vol:34, No.1 (2014), 17-21.
  • [19] A. Ardjouni, A. Djoudi.: Existence and uniqueness of positive solutions for first-order nonlinear Liouville Caputo fractional differential equations, Saeo Paulo J. Math. Sci. Vol:14, No.3 (2020), 381-390.
  • [20] C.B. Zhai and R.T. Jiang, Unique solutions for a new coupled system of fractional differential equations, Adv. Differ. Equ. Vol:2018, No.1 (2018), 1-12.
  • [21] Y.Q. Wang and Y.H. Wu, Existence of uniqueness and nonexistence results of positive solution for fractional differential equations integral boundary value problems, J. Funct. Space. Vol:2018, (2018), 1-7.
  • [22] H. Baghani and J. Alzabut and J. Farokhi-Ostad, et al, Existence and uniqueness of solutions for a coupled system of sequential fractional differential equations with initial conditions, J. Pseudo-Differ. Oper. Vol:11, (2020), 1-11.
  • [23] C.B. Zhai and X.L. Zhu, Unique solution for a new system of fractional differential equations. Adv. Differ. Equ. Vol:2019, No.1 (2019), 1-19.
  • [24] T. Zhu, Existence and uniqueness of positive solutions for fractional differential equations, Bound. Value. Probl. Vol:2019, No.1 (2019), 1-11.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Ling Bai Bu kişi benim

Chengbo Zhaı

Yayımlanma Tarihi 28 Nisan 2021
Gönderilme Tarihi 20 Ocak 2021
Kabul Tarihi 26 Mart 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 1

Kaynak Göster

APA Bai, L., & Zhaı, C. (2021). Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods. Konuralp Journal of Mathematics, 9(1), 176-182.
AMA Bai L, Zhaı C. Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods. Konuralp J. Math. Nisan 2021;9(1):176-182.
Chicago Bai, Ling, ve Chengbo Zhaı. “Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods”. Konuralp Journal of Mathematics 9, sy. 1 (Nisan 2021): 176-82.
EndNote Bai L, Zhaı C (01 Nisan 2021) Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods. Konuralp Journal of Mathematics 9 1 176–182.
IEEE L. Bai ve C. Zhaı, “Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods”, Konuralp J. Math., c. 9, sy. 1, ss. 176–182, 2021.
ISNAD Bai, Ling - Zhaı, Chengbo. “Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods”. Konuralp Journal of Mathematics 9/1 (Nisan 2021), 176-182.
JAMA Bai L, Zhaı C. Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods. Konuralp J. Math. 2021;9:176–182.
MLA Bai, Ling ve Chengbo Zhaı. “Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods”. Konuralp Journal of Mathematics, c. 9, sy. 1, 2021, ss. 176-82.
Vancouver Bai L, Zhaı C. Positive Solutions for a Fractional Thermostat Model via Sum Operators Methods. Konuralp J. Math. 2021;9(1):176-82.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.