### Hardy-Type Inequalities for an Extension of the Riemann- Liouville Fractional Derivative Operators

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**Authors:**S. IQBAL, G. FARID, J. PECARIC AND A. KASHURI

**DOI:**10.46793/KgJMat2105.797I

**Abstract:**

In this paper we present variety of Hardy-type inequalities and their reﬁnements for an extension of Riemann-Liouville fractional derivative operators. Moreover, we use an extension of extended Riemann-Liouville fractional derivative and modiﬁed extension of Riemann-Liouville fractional derivative using convex and monotone convex functions. Furthermore, mean value theorems and n-exponential convexity of the related functionals is discussed.

**Keywords:**

Inequalities, convex functions, Riemann-Liouville fractional derivative.

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