Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 18
Submit an article Journal homepage
185
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Integral representations of scalar delay non-instantaneous impulsive Riemann-Liouville fractional differential equations

Ravi Agarwala Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX, USA;b Distinguished University Professor of Mathematics, Florida Institute of Technology Melbourne, FL, USACorrespondence[email protected]
View further author information
,
S. Hristovac Department of Applied Mathematics and Modeling, University of Plovdiv ”Paisii Hilendarski”, Plovdiv, BulgariaView further author information
&
D. O'Regand School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, IrelandView further author information
Pages 6495-6513 | Received 30 Apr 2020, Accepted 05 Jun 2020, Published online: 21 May 2021

References

  • Agarwal R, Hristova S, O'Regan D. Non-instantaneous impulses in differential equations. Cham, Switzerland: Springer; 2017.
  • Agarwal R, Hristova S, O'Regan D. A survey of Lyapunov functions, stability and impulsive caputo fractional differential equations. Frac Calc Appl Anal. 2016;19(2):290–318.
  • Benchohra M, Seba D. Impulsive fractional differential equations in Banach spaces. Electron J Qual Theory Differ Equ Spec Ed I. 2009;2009(8):1–14.
  • Bonanno G, Rodrguez-Lopez R, Tersian S. Existence of solutions to boundary value problem for impulsive fractional differential equation. Frac Calc Appl Anal. 2014;17(3):717–744.
  • Feckan M, Zhou Y, Wang JR. On the concept and existence of solution for impulsive fractional differential equations. Commun Nonl Sci Numer Simul. 2012;17:3050–3060.
  • Wang JR, Feckan M, Zhou Y. A survey on impulsive fractional differential equations. Frac Calc Appl Anal. 2016;19(4):806–831.
  • Zhang X, Agarwal P, Liu Z, et al., On the fractional differential equations with not instantaneous impulses. Open Phys. 2016;14:676–684.
  • Zhang X, Zhang X, Cao H. On general solution for fractional differential equations with not instantaneous impulses. Fundamenta Inform. 2017;1:355–369.
  • Heymans N, Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheol Acta. 2006;45:765–771.
  • Anguraja A, Kanjanadevia S, Nieto JJ. Mild solutions of Riemann–Liouville fractional differential equations with fractional impulses. Nonlin Anal: Model Control. 2016;22(6):753–764.
  • Chaudharya R, Pandey DN. Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations. Filomat. 2018;32(9):3381–3395.
  • Liu Z, Bin M. Approximmate controlability of impulsive Riemann-Liouvillve fractional differential equations in Banach space. J Integral Eq Appl . 2014;26(4):527–551.
  • Yukunthorn W, Ntouyas SK, Tariboon J. Impulsive multiorders Riemann-Liouville fractional differentialequations. Discrete Dyn Nat Soc. 2015;2015:9, Art. ID 603893.
  • Agarwal R, Hristova S, O'Regan D. Basic concepts of Riemann–Liouville fractional differential equations with non-Instantaneous impulses. Symmetry. 2019;11(5):614, DOI:10.3390/sym11050614
  • Hristova S, Ivanova K. Existence results for Riemann-Liouville fractional differential equations with non-instantaneous impulses (fractional derivative with fixed lower bound at the initial time). AIP Conf. Proc. 2019;2159:030014, DOI:10.1063/1.5127479
  • Li M, Wang JR. Representation of solution of a Riemann-Liouville fractional differential equation with pure delay. Appl Math Lett. 2018;85:118–124.
  • Li M, Wang JR. Finite time stability and relative controllability of Riemann-Liouville fractional delay differential equations. Math. Meth. Appl. Sci. 2019;42:1–17.
  • Diethelm K. The analysis of fractional differential equations. Berlin, Heidelberg: Springer-Verlag; 2010.
  • Podlubny I. Fractional differential equations. San Diego: Academic Press; 1999.
  • Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam: Elsevier; 2006.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.