Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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
Czasopismo
Rocznik
Tom
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
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.