一类非线性弱奇异三重积分不等式中未知函数的估计及其应用

Estimation of Unknown Functions of a Class of Nonlinear Weakly Singular Triple Integral Inequalities and Its Application

研究了一类积分项外包含了非常数项的非线性弱奇异三重积分不等式.利用conformable分数阶导数与conformable分数阶积分的概念与运算法则、变量替换技巧和放大技巧等分析手段,给出了不等式中未知函数的上界估计.最后举例说明所得结果可以用来研究conformable分数阶积分方程解的定性性质.

In this paper,we investigate a class of nonlinear weakly singular triple integral inequalities,which include a nonconstant term outside the integrals.The upper bounds of the embedded unknown functions are estimated explicitly by adopting novel analysis techniques,such as the definitions and rules of conformable fractional differential and conformable fractional integration,the techniques of change of variable,and the method of amplification.Finally,examples are cited to illustrate that the derived results can be applied in the study of qualitative properties of solutions of conformable fractional integral equations.