Sequential Fractional Hybrid Inclusions: A Theoretical Study via Dhage’s Technique and Special Contractions

Sina Etemad, Sotiris K. Ntouyas, Bashir Ahmad, Shahram Rezapour and Jessada Tariboon
Additional contact information
Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Bashir Ahmad: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Shahram Rezapour: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
Jessada Tariboon: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Mathematics, 2022, vol. 10, issue 12, 1-27

Abstract: The most important objective of the present research is to establish some theoretical existence results on a novel combined configuration of a Caputo sequential inclusion problem and the hybrid integro-differential one in which the boundary conditions are also formulated as the hybrid multi-order integro-differential conditions. In this respect, firstly, some inequalities are proven in relation to the corresponding integral equation. Then, we employ some newly defined theoretical techniques with the help of the product operators on a Banach algebra and also with the aid of some special functions including α - ψ -contractions and α -admissible mappings to extract the existence criteria corresponding to the given mixed sequential hybrid BVPs. Some important useful properties such as the approximate endpoint property, ( C α ) -property, and the compactness play a key role in this regard. The final part of the manuscript is devoted to formulating and computing two applicable examples to guarantee the correctness of the obtained results.

Keywords: ?-?-contractive maps; endpoint; Dhage’s fixed point result; sequential derivative; sequential hybrid inclusion problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/12/2090/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/12/2090/ (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:12:p:2090-:d:840462

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 ().