Results 141 to 150 of about 750 (182)

The multi-parameterized integral inequalities for multiplicative Riemann–Liouville fractional integrals

Journal of Mathematical Analysis and Applications
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Tingsong Du
exaly   +2 more sources

A NEW VERSION OF NEWTON’S INEQUALITIES FOR RIEMANN–LIOUVILLE FRACTIONAL INTEGRALS

Rocky Mountain Journal of Mathematics, 2023
The authors give estimates for the modulus of the difference \[ \begin{array}{rl} \mathfrak{D}(\mathfrak{F},\mu,\eta,\alpha):&=\frac{1}{8}\big[\mathfrak{F}(\mu)+3\mathfrak{F}((2\mu+\eta)/3) +3\mathfrak{F}((\mu+2\eta)/3)+\mathfrak{F}(\eta)\big]\\ \\ &-\frac{\Gamma(\alpha+1)}{2(\eta-\mu)^\alpha}\big[\mathscr{J}_{\mu+}^{\alpha} \mathfrak{F}(\eta)+\mathscr{
Hezenci, Fati, Budak, Hüseyin, Kösem, Pinar   +2 more
openaire   +4 more sources

On the Integral Inequalities for Riemann–Liouville and Conformable Fractional Integrals

2018
An integral operator is sometimes called an integral transformation. In the fractional analysis, Riemann–Liouville integral operator (transformation) of fractional integral is defined as $$S_{\alpha }(x)= \frac{1}{\Gamma (x)} \int _{0}^{x} (x-t)^{\alpha -1}f(t)dt$$ where f(t) is any integrable function on [0, 1] and \(\alpha >0\), t is in domain
Emin Ozdemir M., Akdemir A.o., Set E., Ekinci A., Akdemir, Ahmet Ocak, Belirlenecek, Emin Ozdemir, M., Education Faculty, Uludag University, Bursa, Turkey; Akdemir, A.O., Faculty of Science and Letters, Agri Ibrahim Cecen University, Agri, Turkey; Set, E., Faculty of Science and Letters, Ordu University, Ordu, Turkey; Ekinci, A., Faculty of Science and Letters, Ordu University, Ordu, Turkey   +6 more
openaire   +3 more sources

Hermite–Hadamard inequalities for Riemann–Liouville fractional integrals [PDF]

Mathematica Slovaca
Abstract In this paper, we prove some new inequalities of Hermite–Hadamard type for differentiable functions with h-convex derivatives. It is also shown that the newly established inequalities are extension of the existing inequalities in the literature. Finally, we give applications of the new results and outline some future problems.
Ali Muhammad Aamir, Kórus Péter, Nápoles Valdés Juan E.   +2 more
openaire   +1 more source

Rational Approximations of Riemann--Liouville and Weyl Fractional Integrals

Mathematical Notes, 2005
Given \(h\) an \(L_1\)-integrable function on \(I= [a, b]\) and \(\alpha> 0\), set \(f(x)= (P^\alpha_\pm* h)(x)\) where \(P^\alpha_\pm(t)\) denotes either the well known Riemann-Liouville kernel or the Weyl kernel when \(I= [0, 2\pi]\) and \(h\) is a \(2\pi\)-periodic function. Here \(*\) represents the usual ``convolution'' operation.
openaire   +1 more source

SOME PERTURBED NEWTON TYPE INEQUALITIES FOR RIEMANN–LIOUVILLE FRACTIONAL INTEGRALS

Rocky Mountain Journal of Mathematics, 2023
In this paper, the authors establish a new identity for a twice differentiable functions whose second derivatives are convex. Furthermore, using the concepts of Riemann-Liouville fractional integrals, some new perturbed Newton-type inequalities for twice differentiable convex functions are derived and proved.
Hezenci, Fatih, Budak, Hüseyin
openaire   +2 more sources

Bounds of Riemann-Liouville fractional integral operators

2021
Summary: Fractional integral operators play an important role in generalizations and extensions of various subjects of sciences and engineering. This research is the study of bounds of Riemann-Liouville fractional integrals via \((h-m)\)-convex functions. The author succeeded to find upper bounds of the sum of left and right fractional integrals for \((
openaire   +1 more source

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.
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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