Fractional Differential Equations

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.

/pdf/a-sufficient-and-necessary-condition-of-existence-of-blow-up-1o72yzthij.pdf

A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

In this paper, we focus on a generalized singular fractional order Kelvin–Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to the unique solution are established, which are very helpful to govern the process of the Kelvin–Voigt model. At the same time, the corresponding eigenvalue problem is studied and the property of solution for the eigenvalue problem is established. Some examples are given to illuminate the main results.

/pdf/a-singular-fractional-kelvin-voigt-model-involving-a-1p6l602pkq.pdf

A singular fractional Kelvin–Voigt model involving a nonlinear operator and their convergence properties

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder’s fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables.

/pdf/existence-and-asymptotic-analysis-of-positive-solutions-for-3vii2tbyub.pdf

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative. Using a fixed point theorem of Kransnoselskii’s type, the existence and uniqueness results are obtained. Along these lines, different kinds of Hyers–Ulam stability are discussed. An example is given to illustrate the main theorems.

/pdf/analysis-of-coupled-systems-of-implicit-impulsive-fractional-4jsca0abyt.pdf

Analysis of coupled systems of implicit impulsive fractional differential equations involving Hadamard derivatives

In this paper, by using the properties of the Green function, $u_{0}$
 -positive operator and Gelfand’s formula, some properties of the first eigenvalue corresponding to the relevant operator are obtained. Based on these properties, the fixed point index of the nonlinear operator is calculated explicitly and some sufficient conditions for the existence and uniqueness results of positive solution are established.

/pdf/positive-solutions-to-singular-dirichlet-type-boundary-value-puwdqga0es.pdf

Positive solutions to singular Dirichlet-type boundary value problems of nonlinear fractional differential equations

In this paper, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation were obtained; combining fixed point index theorem, sufficient conditions for the existence of positive solutions are established. An example is given to demonstrate the application of our main results.

/pdf/positive-solutions-for-higher-order-nonlocal-fractional-22xmdyjfny.pdf

Positive Solutions for Higher Order Nonlocal Fractional Differential Equation with Integral Boundary Conditions

We begin by introducing some function spaces Lcp(R+),Xcp(J) made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties of Mellin convolution operators mapping on these spaces, next, we derive some new boundedness and continuity properties of Hadamard integral operators mapping on Xcp(J) and Xp(J). Based on this, we investigate a class of boundary value problems for Hadamard fractional differential equations with the integral boundary conditions and the disturbance parameters, and obtain uniqueness results for positive solutions to the boundary value problem under some weaker conditions.

/pdf/properties-of-hadamard-fractional-integral-and-its-ho2pqb4o.pdf

Properties of Hadamard Fractional Integral and Its Application

This research work is dedicated to an investigation for a new kind of boundary value problem of nonlinear fractional differential equation supplemented with general boundary condition. A full analysis of existence and uniqueness of positive solutions is respectively proved by Leray–Schauder nonlinear alternative theorem and Boyd–Wong’s contraction principles. Furthermore, we prove the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of solutions. An example illustrating the validity of the existence result is also discussed.

/pdf/existence-and-stability-analysis-of-solutions-for-a-new-kind-17yhtplo.pdf

Existence and stability analysis of solutions for a new kind of boundary value problems of nonlinear fractional differential equations

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Weiwei Liu

Author Tools

Chat about Author

Papers

Positive solutions to singular Dirichlet-type boundary value problems of nonlinear fractional differential equations

Positive Solutions for Higher Order Nonlocal Fractional Differential Equation with Integral Boundary Conditions

Properties of Hadamard Fractional Integral and Its Application

Existence and stability analysis of solutions for a new kind of boundary value problems of nonlinear fractional differential equations