Fractional version of Ostrowski-type inequalities for strongly p-convex stochastic processes via a k-fractional Hilfer–Katugampola derivative

Abstract

Abstract In the present research, we introduce the notion of convex stochastic processes namely; strongly p-convex stochastic processes. We establish a generalized version of Ostrowski-type integral inequalities for strongly p-convex stochastic processes in the setting of a generalized k-fractional Hilfer–Katugampola derivative by using the Hölder and power-mean inequalities. By using our main results, we derived some known results as special cases and many well-known existing results are also recaptured. It is assumed that this research will offer new guidelines in fractional calculus.

Keywords

• Convex stochastic processes
• Hermite–Hadamard inequality
• Ostrowski inequality