A Fractional q-difference Equation with Integral Boundary Conditions and Comparison Theorem

作者：Ren, Jing; Zhai, Chengbo^*

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2017, 18(7-8): 575-583.

DOI：10.1515/ijnsns-2017-0056

• fractional q-difference equation
• comparison theorem
• integral boundary conditions
• extremal solutions
• iterative method

In this article, we mainly prove the existence of extremal solutions for a fractional q-difference equation involving Riemann-Lioville type fractional derivative with integral boundary conditions. A comparison theorem under weak conditions is also build, and then we apply the comparison theorem, monotone iterative technique and lower-upper solution method to prove the existence of extremal solutions. Moreover, we can construct two iterative schemes approximating the extremal solutions of the fractional q-difference equation with integral boundary conditions. In the last section, a simple example is presented to illustrate the main result.

• 出版日期2017-12
• 单位山西大学