Results on controllability for Sobolev type fractional differential equations of order 1 < r < 2 with finite delay

Yong Ki Ma; Marimuthu Mohan Raja; Kottakkaran Sooppy Nisar; Anurag Shukla; Velusamy Vijayakumar

doi:10.3934/math.2022568

Results on controllability for Sobolev type fractional differential equations of order 1 < r < 2 with finite delay

Yong Ki Ma
, Marimuthu Mohan Raja
, Kottakkaran Sooppy Nisar
, Anurag Shukla
, Velusamy Vijayakumar

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

In this article, exact controllability results for Sobolev fractional delay differential system of 1 < r < 2 are investigated. Fractional analysis, cosine and sine function operators, and Schauder’s fixed point theorem are applied to verify the main results of this study. To begin, we use sufficient conditions to explore the controllability for fractional evolution differential system with finite delay. Lastly, an example is provided to illustrate the obtained theoretical results.

Original language	English
Pages (from-to)	10215-10233
Number of pages	19
Journal	AIMS Mathematics
Volume	7
Issue number	6
DOIs	https://doi.org/10.3934/math.2022568
State	Published - 2022

Keywords

controllability
fractional differential systems
Mainardi’s Wright-type function
mild solutions
Sobolev type

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10.3934/math.2022568

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title = "Results on controllability for Sobolev type fractional differential equations of order 1 < r < 2 with finite delay",

abstract = "In this article, exact controllability results for Sobolev fractional delay differential system of 1 < r < 2 are investigated. Fractional analysis, cosine and sine function operators, and Schauder{\textquoteright}s fixed point theorem are applied to verify the main results of this study. To begin, we use sufficient conditions to explore the controllability for fractional evolution differential system with finite delay. Lastly, an example is provided to illustrate the obtained theoretical results.",

keywords = "controllability, fractional differential systems, Mainardi{\textquoteright}s Wright-type function, mild solutions, Sobolev type",

author = "Ma, \{Yong Ki\} and Raja, \{Marimuthu Mohan\} and Nisar, \{Kottakkaran Sooppy\} and Anurag Shukla and Velusamy Vijayakumar",

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T1 - Results on controllability for Sobolev type fractional differential equations of order 1 < r < 2 with finite delay

AU - Ma, Yong Ki

AU - Raja, Marimuthu Mohan

AU - Nisar, Kottakkaran Sooppy

AU - Shukla, Anurag

AU - Vijayakumar, Velusamy

PY - 2022

Y1 - 2022

N2 - In this article, exact controllability results for Sobolev fractional delay differential system of 1 < r < 2 are investigated. Fractional analysis, cosine and sine function operators, and Schauder’s fixed point theorem are applied to verify the main results of this study. To begin, we use sufficient conditions to explore the controllability for fractional evolution differential system with finite delay. Lastly, an example is provided to illustrate the obtained theoretical results.

AB - In this article, exact controllability results for Sobolev fractional delay differential system of 1 < r < 2 are investigated. Fractional analysis, cosine and sine function operators, and Schauder’s fixed point theorem are applied to verify the main results of this study. To begin, we use sufficient conditions to explore the controllability for fractional evolution differential system with finite delay. Lastly, an example is provided to illustrate the obtained theoretical results.

KW - controllability

KW - fractional differential systems

KW - Mainardi’s Wright-type function

KW - mild solutions

KW - Sobolev type

UR - https://www.scopus.com/pages/publications/85127059244

U2 - 10.3934/math.2022568

DO - 10.3934/math.2022568

M3 - Article

AN - SCOPUS:85127059244

SN - 2473-6988

VL - 7

SP - 10215

EP - 10233

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 6

ER -

Results on controllability for Sobolev type fractional differential equations of order 1 < r < 2 with finite delay

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