Skip to main content
SpringerLink
Log in

Lyapunov-Type Inequalities for Fractional Differential Operators with Non-singular Kernels

  • Conference paper
  • First Online:
Proceedings of the Seventh International Conference on Mathematics and Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1412))

  • 577 Accesses

Abstract

In this paper, we deal with the newly introduced fractional differential operators, which involve exponential and Mittag-Leffler kernels. First, we find Green’s functions and their properties for conjugate and anti-periodic boundary value problems (BVPs) involving Caputo–Fabrizio (CF) and Atangana–Baleanu–Caputo (ABC) fractional derivatives of order \(1 < \varrho \le 2\). Then, we establish Lyapunov-type inequalities (LTIs) for CF and ABC fractional boundary value problems (FBVPs) using the properties of their Green functions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abdeljawad T (2017) Fractional operators with non-singular exponential kernels and a Lyapunov-type inequality. Adv Differ Equ 2017:313

    Article  Google Scholar 

  2. Abdeljawad T (2017) A Lyapunov-type inequality for fractional operators with non-singular Mittag–Leffler kernel. J Inequal Appl 2017:130

    Article  Google Scholar 

  3. Atangana A, Baleanu D (2016) New fractional derivatives with non-local and non-singular kernel: theory and applications to heat transfer model. Therm Sci 20(2):763–769

    Article  Google Scholar 

  4. Baleanu D, Jaiami A, Sajjadi S, Mozyrska D (2019) A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. Chaos 28(8):83–127

    MathSciNet  Google Scholar 

  5. Baleanu D, Basua D, Jonnalagadda JM, Green’s function and an inequality of Lyapunov-type for conformable boundary value problem. Novi Sad J Math. https://doi.org/10.30755/NSJOM.10766

  6. Basua D, Jonnalagadda JM (2019) Lyapunov-type inequality for Riemann-Liouville type fractional boundary value problems. Novi Sad J Math 49:137–152

    MATH  Google Scholar 

  7. Basua D, Jonnalagadda JM, Satpathi DK (2019) Lyapunov-type inequalities for Riemann-Liouville type fractional boundary value problems with fractional boundary conditions. Adv Th Non Anal Appl 3(2):53–63

    MATH  Google Scholar 

  8. Caputo M, Fabrizio M (2015) A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl 1(2):73–85

    Google Scholar 

  9. Ferreira RAC (2013) A Lyapunov-type inequality for a fractional boundary value problem. Fract Calc Appl Anal 16:978–984

    Article  MathSciNet  Google Scholar 

  10. Ferreira RAC (2014) On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function. J Math Anal Appl 412:1058–1063

    Article  MathSciNet  Google Scholar 

  11. Jonnalagadda JM, Debananda B (2020) Fractional analogue of the Lyapunov inequality in conformable sense. J Fract Calc Appl 11(2):23–31

    MathSciNet  MATH  Google Scholar 

  12. Jonnalagadda JM, Debananda B (2020) Lyapunov-type inequalities for Hadamard type fractional boundary value problems. AIMS Math 5(2):1127–1146

    Article  MathSciNet  Google Scholar 

  13. Jonnalagadda JM, Debananda B, Satpathi DK (2021) Lyapunov-type inequality for an anti-periodic conformable boundary value problem. Kragujevac J Math 45:289–298

    Article  MathSciNet  Google Scholar 

  14. Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, Amsterdam

    MATH  Google Scholar 

  15. Liapounoff A (1907) Problème général de la stabilité du mouvement. Ann Fac Sci Toulouse Math 9:203–474

    Article  MathSciNet  Google Scholar 

  16. Ntouyas SK, Ahmad B, Horikis TP (2019) Recent developments of Lyapunov-type inequalities for fractional differential equations. In: Differential and Integral Inequalities. Springer, Cham, pp 619–686

    Google Scholar 

  17. Podlubny I (1999) Fractional differential equations. Academic Press, San Diego

    MATH  Google Scholar 

  18. Saad KM, Atangana A, Baleanu D (2018) New fractional derivatives with non-singular kernel applied to the Burger’s equation. Chaos 28(6):63–109

    Article  MathSciNet  Google Scholar 

  19. Syam MI, Al-Refai M (2019) Fractional differential equations with Atangana-Baleanu fractional derivative: Analysis and applications. Chaos, Solitons Fractals: X 2:100013

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, BITS-Pilani, Hyderabad Campus, Hyderabad, 500078, Telangana, India

    Debananda Basua & Jagan Mohan Jonnalagadda

Authors
  1. Debananda Basua
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jagan Mohan Jonnalagadda
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, India

    Debasis Giri

  2. The University of Texas at San Antonio, San Antonio, TX, USA

    Kim-Kwang Raymond Choo

  3. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India

    Saminathan Ponnusamy

  4. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  5. Department of Computer Engineering, Ondokuz Mayis University, Atakum, Turkey

    Sedat Akleylek

  6. Department of Information Technology, Indian Institute of Engineering Science and Technology, West Bengal, India

    Santi Prasad Maity

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Basua, D., Jonnalagadda, J.M. (2022). Lyapunov-Type Inequalities for Fractional Differential Operators with Non-singular Kernels. In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_58

Download citation

Publish with us

Policies and ethics

Search

Navigation