In this paper, we investigate the approximate controllability of Hilfer fractional differential inclusions with nonlocal conditions. The main techniques rely on the fixed point theorem combined with the semigroup theory, fractional calculus, and multivalued analysis. An interesting example is provided to illustrate the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.

Approximate controllability of Hilfer fractional differential inclusions with nonlocal conditions

This work analyzes the existence and partial-approximate controllability of non-local semi-linear systems involving two Riemann-Liouville fractional derivatives without Lipschitz continuity of non-linearity term. We set an approximate system for the existence of solution. Then under some assumptions, we show that the partial-approximate controllability of the corresponding linear system implies the partial-approximate controllability of the original system. The discussions are based on minimization of functional and fixed point approach. To validate the developed theory, an example is given. 

Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives

In this paper, an evolution system with a Riemann–Liouville fractional derivative is proposed and analyzed. With the help of a resolvent technique, a suitable concept of solutions to this system is formulated and the corresponding existence of solutions is demonstrated. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control result is derived by setting up minimizing sequences twice. Our work essentially generalizes previous results on optimal controls of all evolution systems. Finally, a simple example is presented to illustrate our theoretical results.

Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption

Abstract Time optimal control problems governed by Riemann-Liouville fractional differential system are considered in this paper. Firstly, the existence results are obtained by using the theory of semigroup and Schauder’s fixed point. Secondly, the new approach of establishing time minimizing sequences twice is applied to acquire the time optimal pairs without the Lipschitz continuity of nonlinear function. Moreover, the reflexivity of state space is removed with the help of compact method. Finally, an example is given to illustrate the main conclusions. Our work essentially improves and generalizes the corresponding results in the existing literature.

Time optimal controls for fractional differential systems with Riemann-Liouville derivatives

In this paper, firstly by utilizing the theory of operators semigroup, probability density functions via impulsive conditions, we establish a new PC1−ν-mild solution for impulsive Hilfer fractional differential inclusions. Secondly we prove the existence of mild solutions for the impulsive Hilfer fractional differential inclusions by using fractional calculus, multi-valued analysis and the fixed-point technique. Then under some assumptions, the approximate controllability of associated system are formulated and proved. An example is provided to illustrate the application of the obtained theory. c ©2017 All rights reserved.

/pdf/approximate-controllability-of-impulsive-hilfer-fractional-anxdmhqkpf.pdf

Approximate controllability of impulsive Hilfer fractional differential inclusions

Approximate controllability of Riemann-Liouville fractional differential inclusions

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.

Min Yang

Author Tools

Chat about Author

Papers

Approximate controllability of Riemann-Liouville fractional differential inclusions