1,724 research outputs found
Pseudo asymptotically periodic solutions for fractional integro-differential neutral equations
In this paper, we study the existence and uniqueness of pseudo
-asymptotically -periodic mild solutions of class for fractional
integro-differential neutral equations. An example is presented to illustrate
the application of the abstract results.Comment: It has been accepted for publication in SCIENCE CHINA Mathematic
On a nonlinear neutral stochastic functional integro-differential equation driven by fractional Brownian motion
In this paper, we study the existence and uniqueness of mild solution for a
stochastic neutral partial functional integro-differential equation with delay
in a Hilbert space driven by a fractional Brownian motion and with
non-deterministic diffusion coefficient. We suppose that the linear part has a
resolvent operator. We also establish a sufficient condition for the existence
of the density of a function of the solution. An example is provided to
illustrate the results of this wor
Approximate controllability results for fractional semilinear integro-differential inclusions in Hilbert spaces
In this paper, we consider a class of fractional integro-differential
inclusions in Hilbert spaces. This paper deals with the approximate
controllability for a class of fractional integro-differential control systems.
First, we establishes a set of sufficient conditions for the approximate
controllability for a class of fractional semilinear integro-differential
inclusions in Hilbert spaces. We use Bohnenblust-Karlin's fixed point theorem
to prove our main results. Further, we extend the result to study the
approximate controllability concept with nonlocal conditions. An example is
also given to illustrate our main results.Comment: arXiv admin note: substantial text overlap with arXiv:1502.0008
Existence of mild solutions to Hilfer fractional evolution equations in Banach space
In this paper, we investigate the existence of mild solutions to Hilfer
fractional equation of semi-linear evolution with non-instantaneous impulses,
using the concepts of equicontinuous -semigroup and Kuratowski measure
of non-compactness in Banach space .Comment: 1
Optimal Existence and Uniqueness Theory for the Fractional Heat Equation
We construct a theory of existence, uniqueness and regularity of solutions
for the fractional heat equation , ,
posed in the whole space with data in a class of locally bounded
Radon measures that are allowed to grow at infinity with an optimal growth
rate. We consider a class of nonnegative weak solutions and prove that there is
an equivalence between nonnegative data and solutions, which is given in one
direction by the representation formula, in the other one by the initial trace.
We review many of the typical properties of the solutions, in particular we
prove optimal pointwise estimates and new Harnack inequalities.Comment: 27 page
Fractional order pseudoparabolic partial differential equation: Ulam-Hyers stability
Using Gronwall inequality we will investigate the Ulam-Hyers and generalized
Ulam-Hyers-Rassias stabilities for the solution of a fractional order
pseudoparabolic partial differential equation.Comment: 15 page
On the existence and stability for non-instantaneuos impulsive fractional integrodifferential equation
In this paper, by means of Banach fixed point theorem, we investigate the
existence and Ulam--Hyers--Rassias stability of the non-instantaneous impulsive
integrodifferential equation by means of -Hilfer fractional derivative.
In this sense, some examples are presented, in order to consolidate the results
obtained.Comment: 15 page
S-asymptotically omega-periodic solution for a nonlinear differential equation with piecewise constant argument via S-asymptotically omega-periodic functions in the Stepanov sense
In this paper, we show the existence of function which is not
S-asymptotically omega-periodic, but which is S-asymptotically omega-periodic
in the Stepanov sense. We give sufficient conditions for the existence and
uniqueness of S-asymptotically omega-periodic solutions for a nonautonomous
differential equation with piecewise constant argument in a Banach space when
omega is an integer. This is done using the Banach fixed point Theorem. An
example involving the heat operator is discussed as an illustration of the
theory.Comment: 1
Existence and Uniqueness of Mild Solutions to Neutral SFDE driven by a Fractional Brownian Motion with non-Lipschitz Coefficients
The article presents results on existence and uniqueness of mild solutions to
a class of non linear neutral stochastic functional differential equations
(NSFDEs) driven by Fractional Brownian motion in a Hilbert space with
non-Lipschitzian coefficients. The results are obtained by using the method of
Picard approximation.Comment: 13 page
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
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