Existence and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators

In this article, we are concerned with the existence of mild solutions and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators and nonlocal conditions. The existence results are obtained by first defining Green’s function and approximate controllabili...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2020; no. 1; pp. 1 - 15
Main Authors Bedi, Pallavi, Kumar, Anoop, Abdeljawad, Thabet, Khan, Zareen A., Khan, Aziz
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 31.10.2020
Springer Nature B.V
SpringerOpen
Subjects
Almost sectorial operator
Analysis
Approximate controllability
Banach spaces
Controllability
Difference and Functional Equations
Evolution
Fixed points (mathematics)
Functional Analysis
Hilfer fractional derivative
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlocal conditions
Operators
Ordinary Differential Equations
Partial Differential Equations
Stability
Nonlocal conditions
Almost sectorial operator
Approximate controllability
Hilfer fractional derivative
93B05
26A33
34K37
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Summary:In this article, we are concerned with the existence of mild solutions and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators and nonlocal conditions. The existence results are obtained by first defining Green’s function and approximate controllability by specifying a suitable control function. These results are established with the help of Schauder’s fixed point theorem and theory of almost sectorial operators in a Banach space. An example is also presented for the demonstration of obtained results.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03074-1