NOVEL CHEBYSHEV-TYPE INEQUALITIES FOR THE GENERAL FRACTIONAL-ORDER INTEGRALS WITH THE RABOTNOV FRACTIONAL EXPONENTIAL KERNEL

Abstract

In this paper, we first propose two Chebyshev-type inequalities associated with the general fractional-order (Yang–Abdel–Aty–Cattani) integrals with the Rabotnov fractional-exponential kernel under the condition that [Formula: see text] and [Formula: see text] are synchronous functions. What is more, by the mathematical induction, we prove a new Chebyshev-type inequality in the case that [Formula: see text] be [Formula: see text] positive increasing functions. Finally, we introduce a novel Chebyshev-type inequality via the general fractional-order integrals with the Rabotnov fractional-exponential kernel under the condition that [Formula: see text] and [Formula: see text] are monotonic functions.