Generalized Proportional Caputo Fractional Differential Equations with Noninstantaneous Impulses: Concepts, Integral Representations, and Ulam-Type Stability

Ravi Agarwal, Snezhana Hristova and Donal O’Regan
Additional contact information
Ravi Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
Snezhana Hristova: Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria
Donal O’Regan: School of Mathematical and Statistical Sciences, National University of Ireland, H91 TK33 Galway, Ireland

Mathematics, 2022, vol. 10, issue 13, 1-26

Abstract: The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics, chemistry, biology, etc. In this paper, the presence of noninstantaneous impulses in differential equations with generalized proportional Caputo fractional derivatives is discussed. Generalized proportional Caputo fractional derivatives with fixed lower limits at the initial time as well as generalized proportional Caputo fractional derivatives with changeable lower limits at each impulsive time are considered. The statements of the problems in both cases are set up and the integral representation of the solution of the defined problem in each case is presented. Ulam-type stability is also investigated and some examples are given illustrating these concepts.

Keywords: generalized proportional Caputo fractional derivative; differential equations; noninstantaneous impulses; fixed lower limit of the fractional derivative; changable lower limit of the fractional derivative; existence; Ulam-type stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/13/2315/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/13/2315/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:13:p:2315-:d:854250

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().