Existence and Uniqueness of Non-Negative Solution to a Coupled Fractional q-Difference System with Mixed q-Derivative via Mixed Monotone Operator Method

Yuan Meng, Conghong He, Renhao Ma and Huihui Pang ()
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Yuan Meng: College of Science, China Agricultural University, Beijing 100083, China
Conghong He: College of Science, China Agricultural University, Beijing 100083, China
Renhao Ma: College of Science, China Agricultural University, Beijing 100083, China
Huihui Pang: College of Science, China Agricultural University, Beijing 100083, China

Mathematics, 2023, vol. 11, issue 13, 1-22

Abstract: In this paper, we study a nonlinear Riemann-Liouville fractional a q-difference system with multi-strip and multi-point mixed boundary conditions under the Caputo fractional q-derivative, where the nonlinear terms contain two coupled unknown functions and their fractional derivatives. Using the fixed point theorem for mixed monotone operators, we constructe iteration functions for arbitrary initial value and acquire the existence and uniqueness of extremal solutions. Moreover, a related example is given to illustrate our research results.

Keywords: the coupled Riemann-Liouville fractional q-difference system; the Caputo fractional q-derivative boundary conditions; mixed monotone operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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