Advances in Difference Equations ( IF 3.1 ) Pub Date : 2021-07-13 , DOI: 10.1186/s13662-021-03487-6 Pheak Neang 1 , Kamsing Nonlaopon 1 , Jessada Tariboon 2 , Sotiris K. Ntouyas 3, 4 , Praveen Agarwal 5, 6
Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q-trapezoid and q-midpoint type inequalities. Fractional \((p,q)\)-calculus on finite intervals, particularly the fractional \((p,q)\)-integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional \((p,q)\)-integral on finite intervals. Then, the obtained results are used to derive some fractional \((p,q)\)-trapezoid and \((p,q)\)-midpoint type inequalities.
中文翻译:
通过分数 ( p , q ) $(p,q)$ -calculus 得出的一些梯形和中点类型的不等式
分数阶微积分是研究和应用任意阶积分和导数的数学分析领域。分数q演算已被研究并应用于各种研究课题,包括分数q梯形和q中点型不等式。已经研究了有限区间上的分数\((p,q)\) -演算,特别是分数\((p,q)\) -积分不等式。在本文中,我们研究了有限区间上分数\((p,q)\) -积分形式的连续函数的两个恒等式。然后,将获得的结果用于推导一些分数\((p,q)\) -trapezoid 和\((p,q)\)-中点类型不等式。