Existence and uniqueness of mild solutions for a fractional differential equation under Sturm-Liouville boundary conditions when the data function is of Lipschitzian type

• Autorzy: Harjani Jackie , López Belen , Sadarangani Kishin

Identyfikatory

DOI

10.1515/dema-2020-0014

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fractional differential equation; boundary value problem; mild solution

PL

ułamkowe równanie różniczkowe; zagadnienie brzegowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 167--173
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Harjani Jackie

• Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain

autor

López Belen

• Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain

autor

Sadarangani Kishin

• 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).