Results 181 to 190 of about 357,245 (207)

The Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative on Time Scales

2018
In this chapter we suppose that \(\mathbb {T}\) is a time scale with forward jump operator and delta differentiation operator σ and Δ, respectively.
openaire   +1 more source

The Right Multidimensional Riemann–Liouville Fractional Integral

2016
Here we study some important properties of right multidimensional Riemann–Liouville fractional integral operator, such as of continuity and boundedness.
George A. Anastassiou, Ioannis K. Argyros   +1 more
openaire   +1 more source

Fractional zero-phase filtering based on the Riemann–Liouville integral

Signal Processing, 2014
In this paper, two novel and computationally efficient, zero-phase filtering techniques are proposed based on the Riemann-Liouville integral. Thanks to the reverse phase characteristics of backward filtering, an overall zero-phase effect can be achieved by cascading a fractional forward filtering with a fractional backward filtering, and vice versa ...
Jianhong Wang, Yongqiang Ye, Xiang Pan, Xudong Gao 0002, Chao Zhuang   +4 more
openaire   +2 more sources

Fractional Order Riemann–Liouville Integral Equations

2012
In this chapter, we shall present existence results for some classes of Riemann–Liouville integral equations of two variables by using some fixed-point theorems.
Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata   +2 more
openaire   +1 more source

Riemann–Liouville Fractional Fundamental Theorem of Calculus and Riemann–Liouville Fractional Polya Integral Inequality and the Generalization to Choquet Integral Case

2020
Here we present the right and left Riemann–Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time. Then we establish a Riemann–Liouville fractional Polya type integral inequality with the help of generalised right and left Riemann–Liouville fractional derivatives. The amazing fact here is that
openaire   +1 more source

Some Riemann–Liouville fractional integral inequalities for convex functions

The Journal of Analysis, 2018
We are pleased to investigate some Riemann–Liouville fractional integral inequalities in a very simple and novel way. By using convexity of a function f and a simple inequality over the domain of f we establish some interesting results.
openaire   +2 more sources

Fractional Boole’s inequalities for twice differentiable functions for Riemann–Liouville fractional integrals

Journal of Applied Mathematics and Computing
Boole's type inequalities for first-order differentiable convex functions have been extensively studied, particularly in the context of numerical integration and fractional calculus. However, such inequalities for twice-differentiable functions remain relatively unexplored.
Asia Shehzadi, Hüseyin Budak, Wali Haider, Abdul Mateen, Haibo Chen   +4 more
openaire   +4 more sources

Weight inequalities of the Hardy type for fractional Riemann-Liouville integrals

Siberian Mathematical Journal, 1990
In this paper for the fractional Riemann-Liouville integrals \[ P_ rf(x)=\frac{1}{\Gamma (r)}\int^{x}_{0}(x-t)^{r-1}f(t)dt,\quad r>0, \] the weight estimates of the type \[ (*)\quad (\int^{\infty}_{0}| P_ rf(x)u(x)|^ pdx)^{1/p}\leq C(\int^{\infty}_{0}| f(x)v(x)|^ pdx)^{1/p} \] are studied.
openaire   +2 more sources

Hermite–Hadamard type inequalities for multiplicative Riemann–Liouville fractional integrals

Journal of Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tingsong Du, Yu Peng
openaire   +1 more source

Riemann-Liouville fractional integration and reduced distributions on hyperspheres

Journal of Physics A: Mathematical and General, 1991
Using properties of Dirichlet's iterated integral formula the author shows how the Riemann-Liouville fractional integral unifies arbitrary moment calculations for reduced distributions on hyperspheres. A whole class of problems of this type is then reduced to readily identifiable integral transforms.
openaire   +1 more source