Analytical properties, fractal dimensions and related inequalities of [formula omitted]-Riemann–Liouville fractional integrals

Abstract

In this paper, we rigorously explore (k,h)-Riemann–Liouville fractional integrals applied to continuous functions defined on closed real intervals. Firstly, we delve into the analytical properties of (k,h)-Riemann–Liouville fractional integrals for continuous functions, examining aspects like boundedness, continuity, and bounded variation. Secondly, we derive an upper bound for the upper box dimensions of (k,h)-Riemann–Liouville fractional integral graphs for continuous functions defined on real closed intervals. Finally, we present several applications of (k,h)-Riemann–Liouville fractional integral operators, including the reverse analog Hölder inequality, the reverse analog Minkowski inequality, and Hermite–Hadamard type inequalities.