Results 171 to 180 of about 2,981 (208)

The Solutions of Some Riemann–Liouville Fractional Integral Equations [PDF]

Fractal and Fractional, 2021
In this paper, we propose the solutions of nonhomogeneous fractional integral equations of the form I0+3σy(t)+a·I0+2σy(t)+b·I0+σy(t)+c·y(t)=f(t), where I0+σ is the Riemann–Liouville fractional integral of order σ=1/3,1,f(t)=tn,tnet,n∈N∪{0},t∈R+, and a,b ...
Kamsing Nonlaopon, Somsak Orankitjaroen, Karuna Kaewnimit   +2 more
exaly   +2 more sources

Some integral inequalities for (k, s) – Riemann-Liouville fractional operators [PDF]

Journal of Interdisciplinary Mathematics, 2018
WOS: 000456137400008In this paper, by using a new fractional integral approach of M.Z. Sarikaya et al., we establish new generalized fractional integral inequalities involving (k, s) - Riemann-Liouville integral operators.
Mehmet Zeki Sarikaya, Mohamed Houas
exaly   +3 more sources

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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

The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces III [PDF]

Journal of Mathematical Analysis and Applications
In this manuscript, we examine the continuity properties of the Riemann-Liouville fractional integral for order $α= 1/p$, where $p > 1$, mapping from $L^p(t_0, t_1; X)$ to the Banach space $BMO(t_0, t_1; X)\cap K_{(p-1)/p}(t_0, t_1; X)$. This improvement,
Renato Fehlberg Junior
exaly   +2 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

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 ...
Xudong Gao, Yongqiang Ye, Chao Zhuang
exaly   +2 more sources

Some Riemann–Liouville fractional integral inequalities for convex functions

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.
Ghulam Farid, Farid Ghulam
exaly   +3 more sources

Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions [PDF]

Boundary Value Problems, 2011
This article investigates a boundary value problem of Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions.
Bashir Ahmad, Juan J Nieto, Nieto Juan J   +2 more
exaly   +3 more sources

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.
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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