2020
DOI: 10.1080/17442508.2020.1801685
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Solvability and optimal controls of non-instantaneous impulsive stochastic fractional differential equation of order q ∈ (1,2)

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Cited by 40 publications
(21 citation statements)
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“…The existence and stability of solutions for an optimal control problems derived from an integrodifferential equations with a compact control set in the space L1([0,b];X) studied in Reference 32. In Reference 33, the authors analyzed the stochastic fractional optimal control problems for a systems governed by a class of noninstantaneous impulsive stochastic fractional differential equations in infinite‐dimensional spaces by referring to Krasnoselskii's fixed point theorem, the Laplace transform, and Wiener process. Optimal controls for fractional differential systems of order 1<q<2 by applying the nonlocal conditions, α‐order sine and cosine family, mild solutions, continuous dependence, different fixed point techniques investigated in References 34‐36.…”
Section: Introductionmentioning
confidence: 99%
“…The existence and stability of solutions for an optimal control problems derived from an integrodifferential equations with a compact control set in the space L1([0,b];X) studied in Reference 32. In Reference 33, the authors analyzed the stochastic fractional optimal control problems for a systems governed by a class of noninstantaneous impulsive stochastic fractional differential equations in infinite‐dimensional spaces by referring to Krasnoselskii's fixed point theorem, the Laplace transform, and Wiener process. Optimal controls for fractional differential systems of order 1<q<2 by applying the nonlocal conditions, α‐order sine and cosine family, mild solutions, continuous dependence, different fixed point techniques investigated in References 34‐36.…”
Section: Introductionmentioning
confidence: 99%
“…As a result, a number of academics have recently made major contributions to topics such as electromagnetic control theory, viscoelasticity, image processing, diffusion, signal processing, porous media, biological engineering difficulties, fluid flow, theology, and others. For more specifics, refer to books 1–6 and the research papers 7–21 . Furthermore, fractional differential equations of the Sobolev type are frequently encountered in a variety of applications, including as fluid flow through fissured rocks, thermodynamics, and shear in second order fluids, one can refer to References 8, 11, 14, and 22–26.…”
Section: Introductionmentioning
confidence: 99%
“…In Reference 42, the authors investigate the numerical approximation of solutions to a set of abstract parabolic time optimal control problems using an unbounded control operator. In Reference 17, the authors analyzed the non‐instantaneous impulsive fractional stochastic evolution equations with optimal control problems in infinite‐dimensional spaces by referring to fixed point theorem, the Laplace transform, and Wiener process. Optimal controls for fractional differential systems of order 1<q<2$$ 1<q<2 $$ utilizing the nonlocal conditions, α$$ \alpha $$‐order sine and cosine family, mild solutions, continuous dependence, different fixed point techniques investigated in References 43–45.…”
Section: Introductionmentioning
confidence: 99%
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“…Phenomena with memory and hereditary characteristics that arise in ecology, biology, medicine, electrical engineering, and mechanics, etc, may be well modelled by using fractional differential equations (FDEs for short). For more details on FDEs and its applications, see [1][2][3][4][5] and the references therein. In [6], Hilfer derived a new two-parameter fractional derivative D σ 1 ,σ 2 a + of order σ 1 and type σ 2 , which is called Hilfer fractional derivative that combines the Riemann-Liouville and Caputo fractional derivatives.…”
Section: Introductionmentioning
confidence: 99%