Nonlocal controllability of fractional measure evolution equation

In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x ( t ) d t + ( f ( t , x ( t ) ) + B u ( t ) ) d g ( t ) , t ∈ ( 0 , b ] , x ( 0 ) + p ( x ) = x 0 . The regulated proposition of fractional equation is...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2020; no. 1; pp. 1 - 18
Main Authors Gu, Haibo, Sun, Yu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 10.03.2020
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Controllability
Evolution
Evolution equation
Existence theorems
Fixed points (mathematics)
Fractional calculus
Mathematics
Mathematics and Statistics
Measure of noncompactness
Mild solution
Nonlocal controllability
Evolution equation
Mild solution
Nonlocal controllability
Measure of noncompactness
Fractional calculus
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Summary:In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x ( t ) d t + ( f ( t , x ( t ) ) + B u ( t ) ) d g ( t ) , t ∈ ( 0 , b ] , x ( 0 ) + p ( x ) = x 0 . The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02328-6