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Murugesu, R.
- Nonlocal Cauchy Problem for Fractional Nonlinear Integrodifferential Equations
Abstract Views :201 |
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Authors
R. Murugesu
1,
S. Suguna
1
Affiliations
1 Department of Mathematics, Sri Ramakrishna Mission Vidyalaya, College of Arts and science, Coimbatore 641 020, IN
1 Department of Mathematics, Sri Ramakrishna Mission Vidyalaya, College of Arts and science, Coimbatore 641 020, IN
Source
The Journal of the Indian Mathematical Society, Vol 76, No 1-4 (2009), Pagination: 105-112Abstract
In this paper we discuss the existence and uniqueness of solutions to the nonlocal fractional nonlinear integrodifferential equations
Dqx(t) = f(t, x(t), ∫t0 a(t,s)h(s, x(s))ds), t ∈ [0, T] x(0) + g(x) = x0, where 0 < q < 1
in a Banach space. We use classical tools from functional analysis to obtain the results.
Keywords
Cauchy Problem, Fractional Integrodifferential Quations, Krasnoselkii Theorem.
- Approximate Controllability Results for Neutral Stochastic Differential Equations of Sobolev Type with Unbounded Delay in Hilbert Spaces
Abstract Views :340 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, SRMV College of Arts and Science, Coimbatore-641 020, Tamilnadu, IN
1 Department of Mathematics, SRMV College of Arts and Science, Coimbatore-641 020, Tamilnadu, IN
Source
The Journal of the Indian Mathematical Society, Vol 86, No 1-2 (2019), Pagination: 79-94Abstract
In this paper, we discuss the approximate controllability of the neutral stochastic differential equations of Sobolev type with unbounded delay in Hilbert Spaces. A set of sufficient conditions are established for the existence and approximate controllability of the mild solutions using Krasnoselskii-Schaefer-type fixed point theorems and stochastic analysis theory. An application involving partial differential equation with unbounded delay is addressed.Keywords
Approximate Controllability, Fixed Point Theorems, Stochastic Differential Equation, Mild Solution.References
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