Abstract
Fractional integral inequality plays a significant role in pure and applied mathematics fields. It aims to develop and extend various mathematical methods. Therefore, nowadays we need to seek accurate fractional integral inequalities in obtaining the existence and uniqueness of the fractional methods. Besides, the convexity theory plays a concrete role in the field of fractional integral inequalities due to the behavior of its definition and properties. There is also a strong relationship between convexity and symmetric theories. So, whichever one we work on, we can then apply it to the other one due to the strong correlation produced between them, specifically in the last few decades. First, we recall the definition of phi-Riemann-Liouville fractional integral operators and the recently defined class of convex functions, namely the (sic);-convex functions. Based on these, we will obtain few integral inequalities of Hermite-Hadamard's type for a (sic)-convex function with respect to an increasing function involving the phi-Riemann-Liouville fractional integral operator. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann-Liouville fractional integral inequalities. Finally, application to certain special functions are pointed out.