Results 51 to 60 of about 38,137 (194)

New Approach to Weighted Newton‐Type Inequalities Using Riemann–Liouville Fractional Integrals

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this investigation paper, we present some weighted inequalities Newton‐type for various classes of functions utilizing Riemann–Liouville fractional integrals. The study begins by introducing a positive weighted function to derive a key integral equality essential for proving the main results.
Rubayyi T. Alqahtani, Hüseyin Budak
wiley   +1 more source

Left Riemann–Liouville Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales

Fractal and Fractional, 2022
First, we show the equivalence of two definitions of the left Riemann–Liouville fractional integral on time scales. Then, we establish and characterize fractional Sobolev space with the help of the notion of left Riemann–Liouville fractional derivative ...
Xing Hu, Yongkun Li
doaj   +1 more source

On the confinement of bounded entire solutions to a class of semilinear elliptic systems [PDF]

, 2014
Under appropriate assumptions, we show that all bounded entire solutions to a class of semilinear elliptic systems are confined in a convex domain. Moreover, we prove a Liouville type theorem in the case where the domain is strictly convex.
Sourdis, Christos
core   +1 more source

Fractional Integral Inequalities of Riemann–Liouville Type for Higher‐Order Differentiable Convex Mappings

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we investigate several Riemann–Liouville fractional integral inequalities for higher‐order differentiable functions using a simple and novel approach. First, we present an inequality involving fractional integrals that generalizes the right‐hand side of the fundamental Hermite–Hadamard inequality to higher‐order derivatives ...
Samet Erden, Hüseyin Budak
wiley   +1 more source

Fixed Point Theorems on Controlled Orthogonal δ-Metric-Type Spaces and Applications to Fractional Integrals

Journal of Function Spaces
In this article, we introduce a notion of controlled orthogonal δ-metric-type spaces with an example. Further, we prove a contraction theorem and a generalized fixed point theorem in controlled orthogonal δ-metric-type spaces.
Benitha Wises Samuel, Gunaseelan Mani, Purushothaman Ganesh, Sabri T. M. Thabet, Imed Kedim   +4 more
doaj   +1 more source

A Gradient Bound for the Allen-Cahn Equation Under Almost Ricci Solitons [PDF]

Sahand Communications in Mathematical Analysis
In this paper, we consider positive solutions for the Allen-Cahn equation\begin{equation*}\Delta u+\left(1-u^{2}\right)u=0,\end{equation*}on an almost Ricci soliton   without a boundary. Firstly, using volume comparison Theorem and Sobolev inequality, we
Sakineh Hajiaghasi, Shahroud Azami
doaj   +1 more source

A Liouville type theorem for the Schrödinger operator [PDF]

Proceedings of the American Mathematical Society, 1999
In this paper we prove that the equation Δ u ( x ) + h ( x ) u ( x ) = 0 \Delta u(x)+h(x)u(x)=0 on a complete Riemannian manifold of dimension n n without boundary and with nonnegative Ricci curvature admits no ...
openaire   +3 more sources

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

Existence of Positive Solutions for a Class of m-Point Boundary Value Problems

Advances in Difference Equations, 2008
This paper investigates the existence of positive solutions for a class of second-order singular m-point Sturm-Liouville-type boundary value problems by using fixed point theorem in cones.
Weigao Ge, Xuemei Zhang
doaj   +1 more source

On fractional Cauchy-type problems containing Hilfer's derivative

Electronic Journal of Qualitative Theory of Differential Equations, 2016
In the paper we study fractional systems with generalized Riemann-Liouville derivatives. A theorem on the existence and uniqueness of a solution to a fractional nonlinear ordinary Cauchy problem is proved.
Rafał Kamocki, Cezary Obczyński
doaj   +1 more source