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Novel Lyapunov-type inequality for fractional boundary value problem

Yıl 2019, Cilt: 2 Sayı: 2, 65 - 70, 24.02.2020

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.

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.
Yıl 2019, Cilt: 2 Sayı: 2, 65 - 70, 24.02.2020

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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Rabah Khaldi 0000-0002-6462-4424

Yayımlanma Tarihi 24 Şubat 2020
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 2

Kaynak Göster

APA Khaldi, R. (2020). Novel Lyapunov-type inequality for fractional boundary value problem. Journal of Multidisciplinary Modeling and Optimization, 2(2), 65-70.
AMA Khaldi R. Novel Lyapunov-type inequality for fractional boundary value problem. jmmo. Şubat 2020;2(2):65-70.
Chicago Khaldi, Rabah. “Novel Lyapunov-Type Inequality for Fractional Boundary Value Problem”. Journal of Multidisciplinary Modeling and Optimization 2, sy. 2 (Şubat 2020): 65-70.
EndNote Khaldi R (01 Şubat 2020) Novel Lyapunov-type inequality for fractional boundary value problem. Journal of Multidisciplinary Modeling and Optimization 2 2 65–70.
IEEE R. Khaldi, “Novel Lyapunov-type inequality for fractional boundary value problem”, jmmo, c. 2, sy. 2, ss. 65–70, 2020.
ISNAD Khaldi, Rabah. “Novel Lyapunov-Type Inequality for Fractional Boundary Value Problem”. Journal of Multidisciplinary Modeling and Optimization 2/2 (Şubat 2020), 65-70.
JAMA Khaldi R. Novel Lyapunov-type inequality for fractional boundary value problem. jmmo. 2020;2:65–70.
MLA Khaldi, Rabah. “Novel Lyapunov-Type Inequality for Fractional Boundary Value Problem”. Journal of Multidisciplinary Modeling and Optimization, c. 2, sy. 2, 2020, ss. 65-70.
Vancouver Khaldi R. Novel Lyapunov-type inequality for fractional boundary value problem. jmmo. 2020;2(2):65-70.