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A new fractional integral identity is obtained involving  n -th order differentiable functions and  χ -Riemann–Liouville fractional integrals. Then, some associated estimates of upper bounds involving  γ -preinvex functions are obtained. In order to relate some unrelated results, several special cases are discussed.

mathematical problems in engineering

Estimations of Upper Bounds for <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>n</mi> </math>-th Order Differentiable Functions Involving <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>χ</mi> </math>-Riemann–Liouville Integrals via <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mi>γ</mi> </math>-Preinvex Functions

Estimations of Upper Bounds for n -th Order Differentiable Functions Involving χ -Riemann–Liouville Integrals via γ -Preinvex Functions

Estimations of Upper Bounds for $n$ -th Order Differentiable Functions Involving $χ$ -Riemann–Liouville Integrals via $γ$ -Preinvex Functions