Results 41 to 50 of about 5,661 (277)

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source

Boundary value problems of fractional q-difference equations on the half-line

Boundary Value Problems, 2019
In this paper, we consider the boundary value problem of a class of nonlinear fractional q-difference equations involving the Riemann–Liouville fractional q-derivative on the half-line.
Kuikui Ma, Xinhui Li, Shurong Sun
doaj   +1 more source

On Cauchy–Liouville-type theorems

Advances in Nonlinear Analysis, 2017
Abstract In this paper we explore Liouville-type theorems to solutions of PDEs involving the ϕ-Laplace operator in the setting of Orlicz–Sobolev spaces. Our results extend Liouville-type theorems that have been obtained recently.
Araya Ataklti, Mohammed Ahmed
openaire   +2 more sources

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

The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

Abstract and Applied Analysis, 2013
We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives.
Azizollah Babakhani, Dumitru Baleanu, Ravi P. Agarwal   +2 more
doaj   +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

Existence Results for Fractional Differential Equations Under Weak Topology Features

Pan-American Journal of Mathematics, 2022
Using Krasnoselskii type fixed point theorem under the weak topology, we establish some sufficient conditions to ensure the existence of the weak solutions for kinds of initial value problems of fractional differential equations, involving Riemann ...
Ahmed Hallaci, Aref Jeribi, Bilel Krichen, Bilel Mefteh   +3 more
doaj   +1 more source

Uniform estimates for positive solutions of a class of semilinear elliptic equations and related Liouville and one-dimensional symmetry results [PDF]

, 2013
We consider the semilinear elliptic equation $\Delta u = W'(u)$ with Dirichlet boundary conditions in a smooth, possibly unbounded, domain $\Omega \subset \mathbb{R}^n$. Under suitable assumptions on the potential $W$, including the double well potential
Sourdis, Christos
core  

A Liouville theorem of VT-harmonic map heat flow

, 2023
We proved an Liouville theorem for Backward V T-harmonic map heat flow from evolution manifolds into generalized regular ball. Among others, we also proved an Liouville theorem for V T-harmonic map heat flow from complete manifolds into generalized ...
Cao, Xiangzhi
core  

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