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Here we present Hardy type integral inequalities for Choquet integrals. These are very general inequalities involving convex and increasing functions. Initially we collect a rich machinery of results about Choquet integrals needed next, and we prove also results of their own merit such as, Choquet-Hölder's inequalities for more than two functions and a multivariate Choquet-Fubini's theorem. The main proving tool here is the property of comonotonicity of functions. We finish with independent estimates on left and right Riemann-Liouville-Choquet fractional integrals. [ABSTRACT FROM AUTHOR]

We present here four new generalized Canavati type fractional Taylor's formulae. [ABSTRACT FROM AUTHOR]

Here are presented five new advanced fractional Taylor's formulae un- der as weak as possible assumptions. [ABSTRACT FROM AUTHOR]

In this paper, some new mixed type Riemann-Liouville and Hadamard fractional integral inequalities are established, in the case where the functions are bounded by integrable functions. Moreover, mixed type Riemann-Liouville and Hadamard fractional integral inequalities of Chebyshev type are presented. [ABSTRACT FROM AUTHOR]

Here we present basic Lp fractional integral inequalities for left and right Riemann-Liouville, generalized Riemann-Liouville, Hadamard, Erdelyi- Kober and multivariate Riemann-Liouville fractional integrals. Then we derive basic Lp fractional inequalities regarding the left Riemann-Liouville, the left and right Caputo and the left and right Canavati type fractional derivatives. [ABSTRACT FROM AUTHOR]

Here we present basic Lp fractional integral inequalities for left and right Riemann-Liouville, generalized Riemann-Liouville, Hadamard, Erdelyi-Kober and multivariate Riemann-Liouville fractional integrals. Then we derive basic Lp fractional inequalities regarding the left Riemann-Liouville, the left and right Caputo and the left and right Canavati type fractional derivatives. [ABSTRACT FROM AUTHOR]