Results 51 to 60 of about 1,718 (227)

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

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

Liouville type theorem for a class quasilinear $p$-Laplace type equation on the sphere

, 2022
We use the integral by parts to get a Liouville type theorem for a class quasilinear $p$-Laplace type equation on the sphere, this $p$-Laplace type equation arises from the study of asymptotic behavior near the origin for the semi-linear $p$-Laplace ...
Ma, Xi-Nan, Lin, Daowen
core  

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

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

Composition of Fractional Integral and Derivative Operators: Summarised in Tables

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption.
Arran Fernandez
wiley   +1 more source

Approximation properties of the fractional q-integral of Riemann-Liouville integral type Szasz-Mirakyan-Kantorovich operators

, 2022
In the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szász-Mirakyan-Kantorovich operators. Korovkin-type approximation theorem is given and the order of convergence of these operators are obtained by using ...
Kara, Mustafa
core   +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

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

Multiple positive solutions for nonlinear high-order Riemann–Liouville fractional differential equations boundary value problems with p-Laplacian operator

Boundary Value Problems, 2020
In this paper, we study the existence of multiple positive solutions for boundary value problems of high-order Riemann–Liouville fractional differential equations involving the p-Laplacian operator.
Bibo Zhou, Lingling Zhang, Emmanuel Addai, Nan Zhang   +3 more
doaj   +1 more source