基于katugampola分数阶积分的Hermite-Hadamard型不等式

Hermite-Hadamard Type Inequalities Based on Katugampola Fractional Integrals

分数阶微积分是应用数学的一个重要领域,在自然科学和工程技术等领域有着广泛的实际应用.基于katugampola分数阶积分,利用函数的拟凸性和一些经典不等式,建立了Hermite-Hadamard型不等式.当对参数ρ→1时取极限,就得到了Riemann-Liouville分数阶积分的相应结论.

Fractional calculus is a field of applied mathematics and has practical applications and profound impact in science,engineering,mathematics,economics,and other fields.In this paper,based on Katugampola fractional integrals and by using quasi-convexity and some classical inequalities,the authors establish some new Hermite-Hadamard type inequalities.The obtained inequalities generalize the corresponding results for Riemann-Liouville fractional integrals by taking limits when a parameterρ→1.