Approximate controllability of noninstantaneous impulsive Hilfer fractional integrodifferential equations with fractional Brownian motion

We introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brownian motion. An appropriate set of sufficient conditions is derived for the considered syste...

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Bibliographic Details
Published in:Boundary value problems 2020-07, Vol.2020 (1), p.1-25, Article 120
Main Authors: Ahmed, Hamdy M., El-Borai, Mahmoud M., El Bab, A. S. Okb, Ramadan, M. Elsaid
Format: Article
Language:English
Subjects:
Analysis
Approximate controllability
Approximations and Expansions
Brownian motion
Controllability
Difference and Functional Equations
Fixed points (mathematics)
Fractional Brownian motion
Fractional calculus
Hilfer fractional neutral stochastic differential equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Noninstantaneous impulsive
Nonlocal conditions
Ordinary Differential Equations
Partial Differential Equations
Sadovskii fixed point theorem
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Summary:We introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brownian motion. An appropriate set of sufficient conditions is derived for the considered system to be approximately controllable. For the main results, we use fractional calculus, stochastic analysis, fractional power of operators and Sadovskii’s fixed point theorem. At the end, an example is also given to show the applicability of our obtained theory.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-020-01418-0