Iterative Positive Solutions to a Coupled Riemann-Liouville Fractional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>q</a:mi> </a:math>-Difference System with the Caputo Fractional <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>q</c:mi> </c:math>-Derivative Boundary Conditions
Meng Yuan, Xinran Du, Huihui Pang
Abstract
This paper is devoted to the existence of positive solutions for a nonlinear coupled Riemann-Liouville fractional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M3"> <a:mi>q</a:mi> </a:math> -difference system, with multistrip and multipoint mixed boundary conditions under Caputo fractional <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M4"> <c:mi>q</c:mi> </c:math> -derivative. We obtain the existence of positive solutions and initial iterative solutions by the monotone iteration technique. Then, we also calculate the error limits of the numerical approximation solution by induction. In the end, two examples are given to illustrate the above research results, and in the second example, some graphs of the iterative solutions are also drawn to give a more intuitive sense of the iterative process.