Öz
In this paper, we establish a new Lyapunov-type inequality for a differential equation involving Caputo fractional derivatives subject to non-local boundary conditions. As an application to the corresponding eigenvalue problem is also discussed.
Anahtar Kelimeler
fractional derivative Lyapunov inequality Green’s function eigenvalue problem
Kaynakça
- Abdeljawad, T., Alzabut, J. & Jarad, F. A generalized Lyapunov-type inequality in the frame of conformable derivatives. Adv Differ Equ 2017, 321 (2017)
- R. A. C. Ferreira, Novel Lyapunov-type inequalities for sequential fractional boundary value problems, RACSAM Rev. R. Acad. A, 113 (2019), 171--179.
- A. Guezane-Lakoud, R. Khaldi and D. F.M. Torres, Lyapunov-type inequality for a fractional boundary value problem with natural conditions, SeMA (2018) 75:157--162
- R. Khaldi and A Guezane-Lakoud, On a generalized Lyapunov inequality for a mixed fractional boundary value problem, AIMS Mathematics, 4(3): 506--515.
- R. Khaldi and A Guezane-Lakoud, Lyapunov inequality for a boundary value problem involving conformable derivative, Prog. Frac. Diff. Appl. 3 (2017), No. 4, 323-329.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
- A. M. Lyapunov, Problème général de la stabilité du mouvement, (French Translation of a Russian paper dated 1893), Ann. Fac. Sci. Univ. Toulouse 2 (1907), 27--247, Reprinted as Ann. Math. Studies, No, 17, Princeton, 1947.
- Ntouyas S.K., Ahmad B., Horikis T.P. (2019) Recent Developments of Lyapunov--Type Inequalities for Fractional Differential Equations. In: Andrica D., Rassias T. (eds) Differential and Integral Inequalities. Springer Optimization and Its Applications, vol 151. Springer, Cham
- I. Podlubny, Fractional Differential Equation, Academic Press, Sain Diego, 1999.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
Öz
Kaynakça
- Abdeljawad, T., Alzabut, J. & Jarad, F. A generalized Lyapunov-type inequality in the frame of conformable derivatives. Adv Differ Equ 2017, 321 (2017)
- R. A. C. Ferreira, Novel Lyapunov-type inequalities for sequential fractional boundary value problems, RACSAM Rev. R. Acad. A, 113 (2019), 171--179.
- A. Guezane-Lakoud, R. Khaldi and D. F.M. Torres, Lyapunov-type inequality for a fractional boundary value problem with natural conditions, SeMA (2018) 75:157--162
- R. Khaldi and A Guezane-Lakoud, On a generalized Lyapunov inequality for a mixed fractional boundary value problem, AIMS Mathematics, 4(3): 506--515.
- R. Khaldi and A Guezane-Lakoud, Lyapunov inequality for a boundary value problem involving conformable derivative, Prog. Frac. Diff. Appl. 3 (2017), No. 4, 323-329.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
- A. M. Lyapunov, Problème général de la stabilité du mouvement, (French Translation of a Russian paper dated 1893), Ann. Fac. Sci. Univ. Toulouse 2 (1907), 27--247, Reprinted as Ann. Math. Studies, No, 17, Princeton, 1947.
- Ntouyas S.K., Ahmad B., Horikis T.P. (2019) Recent Developments of Lyapunov--Type Inequalities for Fractional Differential Equations. In: Andrica D., Rassias T. (eds) Differential and Integral Inequalities. Springer Optimization and Its Applications, vol 151. Springer, Cham
- I. Podlubny, Fractional Differential Equation, Academic Press, Sain Diego, 1999.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 24 Şubat 2020 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 2 |
