一类弱奇异积分不等式及其应用  

A Class of Weakly Singular Integral Inequality and Its Application

作　　者：钟华[1] 王五生[1] 

机构地区：[1]河池学院数学与统计学院,广西宜州546300

出　　处：《中北大学学报（自然科学版）》2016年第5期446-450,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161018);广西自然科学基金资助项目(2012GXNSFAA053009);广西高等学校科研项目(KY2015ZD103;KY2015YB257)

摘　　要：研究了一类非线性弱奇异Volterra-Fredholm型迭代积分不等式,把不含奇性的积分不等式推广成弱奇异积分不等式,把线性奇异积分不等式推广成非线性积分不等式.根据分数阶导数和分数阶积分的定义和运算法则,运用放大、积分、微分、变量替换、反函数等分析技巧给出了不等式中未知函数的估计,推广了参考文献的结果.最后,为了说明结果的有效性,用所得结果给出了一类非线性Volterra-Fredholm分数阶积分方程解的估计.A class of iterated nonlinear Volterra-Fredholm type integral inequality with weak singularity was investigated,which generalized the integral inequality without singularity to the integral inequality with weak singularity,and generalized the linear integral inequality with weak singularity to the nonlinear integral inequality with weak singularity.By the definitions and rules of fractional differential and fractional integral,adopting analysis techniques,such as amplification method,differential and integration,change of variable,inverse function,the estimation of the unknown functions is given.The results of the references are generalized.Finally,to illustrate the validity of the results,our result is used to give the estimation of the solutions of a class of nonlinear Volterra-Fredholm type fractional integral equations.

关 键 词：弱奇异积分不等式 分析技巧 分数阶积分方程 估计 

分 类 号：O175.5[理学—数学]