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

Abstract

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.