Theoretical Results on Positive Solutions in Delta Riemann–Liouville Setting

Pshtiwan Othman Mohammed (), Ravi P. Agarwal, Majeed A. Yousif, Eman Al-Sarairah, Alina Alb Lupas () and Mohamed Abdelwahed
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Pshtiwan Othman Mohammed: Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
Ravi P. Agarwal: Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA
Majeed A. Yousif: Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq
Eman Al-Sarairah: Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi P.O. Box 127788, United Arab Emirates
Alina Alb Lupas: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Mohamed Abdelwahed: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2024, vol. 12, issue 18, 1-16

Abstract: This article primarily focuses on examining the existence and uniqueness analysis of boundary fractional difference equations in a class of Riemann–Liouville operators. To this end, we firstly recall the general solution of the homogeneous fractional operator problem. Then, the Green function to the corresponding fractional boundary value problems will be reconstructed, and homogeneous boundary conditions are used to find the unknown constants. Next, the existence of solutions will be studied depending on the fixed-point theorems on the constructed Green’s function. The uniqueness of the problem is also derived via Lipschitz constant conditions.

Keywords: Riemann–Liouville operators; Green’s function (GF); fixed-point theorem; existence and uniqueness solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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