Expanding the analytical aspect of mathematics enables researchers to study more cosmic phenomena, especially with regard to the applied sciences related to fractional calculus. In the present paper, we establish some Chebyshev-type inequalities in the case synchronous functions. In order to achieve our goals, we use k , ψ -proportional fractional integral operators. Moreover, we present some special cases.

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In this paper, we establish Iyengar type inequalities utilizing ψ-Caputo fractional derivatives that is, fractional derivative of a function with respect to another function, which is generalization of some known fractional derivatives such as Riemann-Liouville, Hadamard, Erdélyi-Kober. The inequalities in this article are with respect to L p norms, 1 ≤ p ≤ ∞. The tools used in the analysis are based on Taylor's formulae for ψ-Caputo fractional derivatives.