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Abstrakty
In this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of Lipschitzian type. Moreover, we present an application of our result to the eigenvalues problem and its connection with a Lyapunov-type inequality.
Wydawca
Czasopismo
Rocznik
Tom
Strony
167--173
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
autor
- Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
autor
- Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
Bibliografia
- [1] W. G. Kelley and A. C. Peterson, The Theory of Differential Equations, 2nd edn, Universitext, Springer-Verlag, New York, 2010.
- [2] Rui A. C. Ferreira, Existence and uniqueness of solutions for two-point fractional boundary value problems, Electron. J. Diff. Eq. 2016(2016), no. 202, 1-5.
- [3] B. Ahmad, Sharp estimates for the unique solution of two-point fractional-order boundary value problems, Appl. Math. Lett. 65(2017), 77-82.
- [4] Rui A. C. Ferreira, Note on a uniqueness result for a two-point fractional boundary value problem, Appl. Math. Lett. 90(2019), 75-78.
- [5] M. Jleli and B. Samet, Existence of positive solutions to a coupled system of fractional differential equations, Math. Methods Appl. Sci. 38(2015), no. 6, 1014-1031.
- [6] Rui A. C. Ferreira, On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function, J. Math. Anal. Appl. 412(2014), no. 2, 1058-1063.
- [7] J. Rong and C. Bai, Lyapunov-type inequality for a fractional differential equation with fractional boundary condition, Adv. Differ. Equ. 2015(2015), 82, DOI: 10.1186/s13662-015-0430-x.
- [8] M. Jleli, D. O’Regan, and B. Samet, Lyapunov-type inequalities for coupled systems of nonlinear fractional differential equations via afixed point approach, J. Fixed Point Theory Appl. 21(2019), 45, DOI: 10.1007/s11784-019-0683-1.
- [9] B. López, J. Rocha, and K. Sadarangani, Lyapunov-type inequalities for a class of fractional boundary value problems with integral boundary conditions, Math. Methods Appl. Sci. 42(2019), no. 1, 49-58.
- [10] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, in North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., 2006.
- [11] Y. Wang, S. Liang, and C. Xia, A Lyapunov-type inequality for a fractional differential equation under Sturm-Liouville boundary conditions, Math. Inequal. Appl. 20(2017), no. 1, 139-148.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-65283d36-084f-4bdc-95f2-882ba0189766