Abstract
In this paper estimations in general form of sum of left and right sided Riemann-Liouville (RL) fractional integrals for convex functions are studied. Also some similar fractional inequalities for functions whose deriva tives in absolute value are convex, have been obtained. Associated fractional integral inequalities provide the bounds of different known fractional inequal ities. These results may be useful in in the study of uniqueness solutions of fractional differential equations and fractional boundary value problems.
Highlights
Fractional calculus is applied in almost all disciplines of engineering and modern sciences
Fractional di¤erential equations and fractional dynamics are due to fractional calculus
In this paper we study a general form of Riemann-Liouville (RL) fractional integrals via convex functions
Summary
Fractional calculus is applied in almost all disciplines of engineering and modern sciences. Fractional integral inequalities occur by default in the study of convex and related functions due to applications of de...nitions of fractional integral as well as fractional derivative operators. In this paper we study a general form of Riemann-Liouville (RL) fractional integrals via convex functions. A more general de...nition of (RL) fractional integral is the Riemann-Liouville fractional integral with respect an increasing function (see, [9]). The paper is organized as follows: In Section 2, bounds of sum of the left and right sided (RL) k-fractional integrals in general form de...ned in De...nition 4 have been established. The presented results are useful in the study of fractional di¤erential equations and fractional boundary value problems They provide the estimations of Riemann-Liouville fractional integrals which are published in [4] and some results of [3].
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