Results 11 to 20 of about 357,245 (207)

Maclaurin-type inequalities for Riemann-Liouville fractional integrals [PDF]

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, 2023
The authors give estimates for the modulus of the difference \[ D(f,a,b,\alpha):=\frac{1}{8}\big[3f((5a+b)/6)+2f((a+b)/2)+2f((a+3b)/6)\big]-\frac{\Gamma(\alpha+1)}{2(b-a)^\alpha}\big[J_{a+}^{\alpha} f(b)+J_{b-}^{\alpha} f(a)\big] \] where \(f\in L_1[a,b]\) and \[ J_{a+}^{\alpha}f(x):=\frac{1}{\Gamma(\alpha)}\int_a^x (x-t)^{\alpha-1}f(t)dt,\,\,x>a \] \[
Hezenci, Fatih, Budak, Hüseyin
openaire   +3 more sources

On some generalized integral inequalities for Riemann-Liouville fractional integrals [PDF]

Filomat, 2015
In this paper, we give a generalized Montogomery identities for the Riemann-Liouville fractional integrals. We also use this Montogomery identities to establish some new Ostrowski type integral inequalities.
Sarikaya, Mehmet Zeki, Filiz, Hatice, Kiris, Mehmet Eyup   +2 more
openaire   +4 more sources

Sándor’s inequality for Riemann-Liouville fractional integrals

Miskolc Mathematical Notes
The Sándor inequality is a highly significant result in both pure and applied mathematics, providing an upper bound for the mean square of a positive convex function. This paper presents an extension of the Sándor inequality to the case of fractional integrals in the sense of Riemann-Liouville, as well as a generalization for any ...
Meftah, Badreddine, Saleh, Wedad, LAKHDARI, Abdelghani   +2 more
openaire   +3 more sources

Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions [PDF]

Fractal and Fractional, 2022
In this paper, we prove some new Newton’s type inequalities for differentiable convex functions through the well-known Riemann–Liouville fractional integrals.
Thanin Sitthiwirattham, Kamsing Nonlaopon, Muhammad Aamir Ali, Hüseyin Budak   +3 more
doaj   +2 more sources

Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals

Communications in Advanced Mathematical Sciences
In this paper, some Euler-Maclaurin-type inequalities are established by using $h-$convex functions involving Riemann-Liouville fractional integrals.
Hüseyin Budak, Fatih Hezenci
doaj   +2 more sources

Inequalities for Co-ordinated m−Convex Functions via Riemann-Liouville Fractional Integrals [PDF]

International Journal of Analysis and Applications, 2014
In this paper, we prove some new inequalities of Hadamard-type for m−convex functions on the co-ordinates via Riemann-Liouville fractional integrals.
Çetin Yildiz, Mevlüt Tunc, Havva Kavurmaci   +2 more
doaj   +4 more sources

On a Fractional Differential Equation with r-Laplacian Operator and Nonlocal Boundary Conditions

Mathematics, 2022
We study the existence and multiplicity of positive solutions of a Riemann-Liouville fractional differential equation with r-Laplacian operator and a singular nonnegative nonlinearity dependent on fractional integrals, subject to nonlocal boundary ...
Johnny Henderson, Rodica Luca, Alexandru Tudorache   +2 more
doaj   +1 more source

Numerical Approximations of the Riemann–Liouville and Riesz Fractional Integrals

Informatica, 2023
In this paper, the numerical algorithms for calculating the values of the left- and right-sided Riemann–Liouville fractional integrals and the Riesz fractional integral using spline interpolation techniques are derived. The linear, quadratic and three variants of cubic splines are taken into account.
Mariusz Ciesielski, Grzegorz Grodzki
openaire   +1 more source

A Note on Fractional Midpoint Type Inequalities for Co-ordinated (s1, s2)-Convex Functions

Cumhuriyet Science Journal, 2022
In the present paper, some Hermite-Hadamard type inequalities in the case of differentiable co-ordinated (s_1," " s_2)-convex functions are investigated.
Fatih Hezenci
doaj   +1 more source

On a system of Riemann–Liouville fractional differential equations with coupled nonlocal boundary conditions

Advances in Difference Equations, 2021
We investigate the existence of solutions for a system of Riemann–Liouville fractional differential equations with nonlinearities dependent on fractional integrals, subject to coupled nonlocal boundary conditions which contain various fractional ...
Rodica Luca
doaj   +1 more source