A new version of Ostrowski type integral inequalities for different differentiable mapping

In this paper, improved and generalized version of Ostrowski’s type inequalities is established. The parameters used in the peano kernels help us to obtain previous results. The obtained bounds are then applied to numerical integration.

Generalized Fractional Ostrowski's Type Inequalities Involving Riemann-Liouville Fractional Integration

Fractional calculus has applications in many practical problems such as electromagnetic waves, visco-elastic systems, quantum evolution of complex systems, diffusion waves, physics, engineering, finance, social sciences, economics, mathematical biology, and chaos theory. Theories of inequality are growing rapidly; the fractional version of Ostrowski's type inequality is one of them. In this chapter, the author firstly presents some generalized Montgomery identities for Riemann-Liouville fractional integrals, which are designed by using a new and special type of Peano kernels. Secondly, inequalities via convex function are also discussed. In addition, some general fractional representation formulae are studied for a function in terms of the fractional Riemann-Liouville integrals of different orders and its ordinary derivatives. Moreover, by utilizing Montgomery identities, some new fractional versions of Ostrowski's type integral inequalities are established. Some well-known results are deduced as special cases from the results are developed here.