Investigation of the Fractional Strongly Singular Thermostat Model via Fixed Point Techniques

Mohammed K. A. Kaabar, Mehdi Shabibi, Jehad Alzabut, Sina Etemad, Weerawat Sudsutad, Francisco Martínez and Shahram Rezapour
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Mohammed K. A. Kaabar: Faculty of Science, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia
Mehdi Shabibi: Department of Mathematics, Mehran Branch, Islamic Azad University, Mehran, Iran
Jehad Alzabut: Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
Weerawat Sudsutad: Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Francisco Martínez: Department of Applied Mathematics and Statistics, Technological University of Cartagena, 30203 Cartagena, Spain
Shahram Rezapour: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran

Mathematics, 2021, vol. 9, issue 18, 1-21

Abstract: Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving ? - ? -contractions and ? -admissible maps. Further, we establish the similar results for the hybrid version of the given fractional strongly singular thermostat control model. Some examples are studied to illustrate the consistency of our results.

Keywords: boundary conditions; hybrid differential equation; fractional thermostat model; strong singularity; the Caputo derivative; ? - ? -contraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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