无穷区间上迭代泛函分数阶 q -差分方程的正解

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中图分类号：0175.8 文献标识码：A DOI：10.7535/hbkd.2026yx02006

Abstract：In order to expand the theory of fractional q -difference equations，the existence of solutions to boundary value problems of a class of iterative functional higher-order fractional q -difference equations with integral boundary conditions on infinite ntervals was studied.Firstly，the Green’s functionoffractional diferenceequationboundaryvalue problem was calculatedanditsproperties werestudiedSecondly，anappopriateBanach spaceandnormwere introduced，andtheitegral operatorwas then constructed.Thirdly，the existence theorem of positivesolution of the problemwas obtainedby using monotoneiterativetechniqueandupperandlowersolution method.Finally，theeffectivenessand practicabilityof themain results were verified byaconcrete example.The results show thatunder certain growth conditions of the nonlinear term ， thereexists at leastone positive solution totheboundary value problemof iterativefunctional fractional quantum diference equations on infinite intervals. The research results enrich the solvability theory of fractional q -difference equations，reflect the influenceoffeedback iterativetermsontheexistenceofsolutions，and providecertain theoretical guidancefortheaplicationof iterative functional fractional q -difference equations in many fields such as control engineering，biomedicine，population theory， and social economy.

Keywords：nonlinearfunctionalanalysis；upperand lower solution；monotone iterativetechnique；infinite intervals；integral boundary conditions

量子微积分，亦称 q -微积分，20 世纪初由JACKSON[1]提出，广泛应用于数学、量子理论和力学等领域[2-5]。（剩余9080字）