Generalization of Ostrowski’s Type Inequality Via Riemann-Liouville Fractional Integral and Applications in Numerical Integration, Probability Theory and Special Means

Abstract

We apply Riemann-Liouville fractional integral to get a new generalization of Ostrowski’s type integral inequality. We may prove new estimates for the remainder term of the midpoint’s, trapezoid’s, & Simpson’s formulae as a result of the generalization. Our estimates are generalized and recaptured some previously obtained estimates. Applications are also deduced for numerical integration, probability theory and special means.

Key words and phrases. Fractional Calculus, Riemann-Liouville fractional integral operator, Ostrowski’s inequality, Error bounds, Probability density function, Numerical integration, Special means.

2010 Mathematics Subject Classification. 26D10, 26D15, 26D20, 26A15, 26A42, 26A99