Skip to main content
SpringerLink
Log in

Existence Results of Mild Solutions for Impulsive Fractional Differential Equations with Almost Sectorial Operators

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

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1262))

Abstract

This paper is concerned with the existence and uniqueness of mild solutions for a class of fractional impulsive semilinear differential equations using the concepts of almost sectorial operators. The results are established by using Banach contraction principle and Schauder’s fixed point theorem.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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

Similar content being viewed by others

References

  1. Da Prato G, Sinestrari E (1987) Differential operators with non-dense domain. Ann. Scuola Norm. Sup. Pisa cl. sci. 14:285–344

    MathSciNet  MATH  Google Scholar 

  2. Lunardi A (1995) Analytic semigroups and optimal regularity in parabolic problems. Birkhauser Verlag, Basel

    Book  Google Scholar 

  3. Von Wahl, W (1972) Gebrochene potenzen eines elliptischen operators und parabolische Differentialgleichungen in Raumen holderstetiger Funktionen. Nachr. Akad. Wiss. Gottingen, Math.-Phys. Klasse 11, 231–258

    Google Scholar 

  4. Periago F, Straub B (2002) A functional calculus for almost sectorial operators and applications to abstract evolution equations. J. Evol. Equ. 2:41–68

    Article  MathSciNet  Google Scholar 

  5. Dlotko T (2007) Semilinear Cauchy problems with almost sectorial operaors. Bull. Pol. Acad. Sci. Math. 55:333–346

    Article  MathSciNet  Google Scholar 

  6. Okazawa N (1974) A generation theorem for semigroups of growth order \(\alpha \). Tohoku Math. L. 26:39–51

    Article  MathSciNet  Google Scholar 

  7. Periago F (2003) Global existence, uniqueness and continuous dependence for a semilinear initial value problem. J. Math. Anal. Appl. 280:413–423

    Google Scholar 

  8. Taira K (1989) The theory of semigroups with weak singularity and its applications to partial differential equations. Tsukuba J. Math. 13:513–562

    Article  MathSciNet  Google Scholar 

  9. Wang Rong-Nian, Chen De-Han, Xiaon Ti-jun (2012) Abstract fractional cauchy problems with almost sectorial operators. Journal of Differential Equations. 252:202–235

    Article  MathSciNet  Google Scholar 

  10. Lu Zhang., Yong Zhou.: Fractional cauchy problems wuth almost sectorial operators. 257, 145-157 (2015). https://doi.org/10.1016/j.amc.2014.07.024

  11. Xiao-LiDing., Bashir Ahmad.: Analytical solutions to fractional evolution equations with almost sectorial operators. Advances in Difference Equations, 2016:203 (2016). https://doi.org/10.1186/s13662-016-0927-y

  12. DiZhang., Yue Liang.:Existence and controllability of fractional evolution equation with sectorial operator and impulse. Advances in Difference Equations. 2018:219 (2018). https://doi.org/10.1186/s13662-018-1664-1

  13. Podlubny I (1993) Fractional Differential Equations. Academic Press, New York

    MATH  Google Scholar 

  14. Ahmed B, Sivasundaram S (2010) Existence of solutions for Integral boundary value problems of fractional order. Nonlinear Analysis: Hybrid Systems. 4:134–141

    MathSciNet  MATH  Google Scholar 

  15. Lakshmikantham V, Bainov DD, Simenov PS (1989) Theory of Impulsive Differential Equations. World Scientific, Singapore

    Book  Google Scholar 

  16. Mophou G (2010) Existence and uniqueness of mild solutions to impulsive fractional differential equations. Nonlinear Analysis: Theory, Methods and Applications. 72:1604–1615

    Article  MathSciNet  Google Scholar 

  17. Wang RN, Chen DH, Xiao TJ (2012) Abstraft fractional cauchy problems with almost sectorial operators. Journal of Differential Equations. 252:202–235

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Department of Mathematics, MES Mampad College, Malappuram, Kerala, India

    M. C. Ranjini

Authors
  1. M. C. Ranjini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. C. Ranjini .

Editor information

Editors and Affiliations

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

    Debasis Giri

  2. School of Computing and Information Systems, University of Melbourne, Melbourne, VIC, Australia

    Rajkumar Buyya

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

    S. Ponnusamy

  4. Department of Computer Science and Engineering, Maulana Abul Kalam Azad University of Technology, Haringhata, West Bengal, India

    Debashis De

  5. Unconventional Computing Laboratory, Department of Computer Science and Creative Technologies, University of the West of England, Bristol, UK

    Andrew Adamatzky

  6. Faculty of Science, Engineering and Built Environment, Deakin University Geelong, Geelong, VIC, Australia

    Jemal H. Abawajy

Rights and permissions

Reprints and permissions

Copyright information

© 2021 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

Ranjini, M.C. (2021). Existence Results of Mild Solutions for Impulsive Fractional Differential Equations with Almost Sectorial Operators. In: Giri, D., Buyya, R., Ponnusamy, S., De, D., Adamatzky, A., Abawajy, J.H. (eds) Proceedings of the Sixth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1262. Springer, Singapore. https://doi.org/10.1007/978-981-15-8061-1_41

Download citation

Publish with us

Policies and ethics

Search

Navigation