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Solutions of a coupled system of hybrid boundary value problems with Riesz-Caputo derivative

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Języki publikacji
EN
Abstrakty
EN
Riesz-Caputo fractional derivative refers to a fractional derivative that reflects both the past and the future memory effects. This study gives sufficient conditions for the existence of solutions for a coupled system of fractional order hybrid differential equations involving the Riesz-Caputo fractional derivative. For this motive, the results are obtained via classical results due to Dhage.
Wydawca
Rocznik
Strony
art. no. 20230125
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • School of Science, Tianjin University of Technology, Tianjin 300384, China
autor
  • School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, China
autor
  • School of Science, Tianjin University of Technology, Tianjin 300384, China
Bibliografia
  • [1] R. Hilfer, (Ed.), Application of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [2] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V, Amsterdam, 2006.
  • [3] G. A. Anastassiou, On right fractional calculus, Chaos Solitons Fractals 42 (2009), no. 1, 365–376.
  • [4] B. Ahmad and J. J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl. 58 (2009), 1838–1843.
  • [5] X. Fu, Existence results for fractional differential equations with three-point boundary conditions, Adv. Differential Equations 2013 (2013), Article No. 257, 1–15.
  • [6] M. Benchohra, J. R. Graef, and S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal. 87 (2008), 851–863.
  • [7] B. C. Dage, Basic results in the theory of hybrid differential equations with linear perturbations os second type, Tamkang J Math. 44 (2012), no. 2, 171–186.
  • [8] R. A. Khan and K. Shah, Existence and uniqueness of solutions to fractional order multi-point boundary value problems, Commun. Appl. Anal. 19 (2015), 515–526.
  • [9] H. Lu, S. Sun, D. Yang, and H. Teng, Theory of fractional hybrid differential equations with linear perturbations of second type, Boundary Value Problems. 23 (2013), 1–16.
  • [10] B. Ahmad, S. K. Ntouyas, and J. Tariboon, A nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations, Acta Math. Sci. 36 (2016), no. 6, 1631–1640.
  • [11] Z. Sanli, Simpson type Katugampola fractional integral inequalities via Harmonic convex functions, Malaya J. Mat. 10 (2022), 364–373.
  • [12] C. Y. Gu, J. Zhang, and G. C. Wu, Positive solutions of fractional differential equations with the Riesz space derivative, Appl. Math. Lett. 95 (2019), 59–64.
  • [13] S. S. Ray, Soliton solutions of nonlinear and nonlocal Sine-Gordon equation involving Riesz space fractional derivative, Z. Naturforsch. 70 (2015), 659–667.
  • [14] Q. Yang, F. Liu, and I. Turner, Numerical methods for fractional partial differential equations with Riesz space fractional derivatives Appl. Math. Model. 34 (2010), 200–218.
  • [15] R. Almeida, Fractional variational problems with the Riesz-Caputo derivative, Appl. Math. Lett. 25 (2012), 142–148.
  • [16] A. Ardjouni and M. Haoues, Existence and monotonicity of positive solutions for hybrid Caputo-Hadamard fractional integro-differential equations, Malaya J. Mat. 9 (2021), 168–180.
  • [17] M. Caputo, Linear Models of dissipation whose Q is almost frequency independent, Int. J. Geo. Sci. 13 (1967), no. 5, 529–539.
  • [18] B. C. Dhage, A fixed point theorem in Banach algebras involving three operators with applications, Kyungpook Math. J. 44 (2004), 145–155.
  • [19] B. C. Dhage, A nonlinear alternative in Banach algebras with applications to functional differential equations, Nonlinear Funct. Anal. Appl. 8 (2004), 563–575.
  • [20] B. C. Dhage, Fixed point theorems in ordered Banach algebras and applications, J. Panam. Math. 9 (1999), 93–102.
  • [21] M. Houas, Solvability of a system of fractional hybrid differential equations, Commun. Optim. Theory 2018 (2018), 1–9.
  • [22] C. Derbazi, H. Hammouche, M. Benchohra, and Y. Zhou, Fractional hybrid differential equations with three-point boundary hybrid conditions, Adv. Differential Equations 2019 (2019), Article No. 125, 1–11.
  • [23] D. Baleanu, H. Khan, H. Jafari, R. A. Khan, and M. Alipour, On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions, Adv. Differential Equations 2015 (2015), Article No. 318, 1–14.
  • [24] N. Adjimi, M. Benbachir, and K. Guerbati, Existence results for x-Caputo hybrid fractional integro-differential equations, Malaya J. Mat. 9 (2021), 46–54.
  • [25] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [26] Samina, K. Shah, and R. A. Khan, Stability theory to a coupled system of nonlinear fractional hybrid differential equations, Indian J. Pure Appl. Math. 51 (2020), no. 2, 669–687.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6899ac9b-5e15-4272-8b83-3a9645412158
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