Results 21 to 30 of about 442,403 (170)

Mild solutions of non‐Lipschitz stochastic integrodifferential evolution equations [PDF]

Mathematical Methods in the Applied Sciences, 2016
In this work, we study the existence and uniqueness of mild solutions for stochastic partial integrodifferential equations under local non‐Lipschitz conditions on the coefficients. Our analysis makes use of the theory of resolvent operators as developed by R. Grimmer as well as a stopping time technique.
Abdoul Diop, Mamadou, Caraballo, Tomás, Mané, Aziz   +2 more
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A Priori Uniform Bounds as Measure-Theoretic Tools: Long-Term Analysis via Classical-Enhanced Synthesis

Mathematics
This work presents a systematic study of nonlinear differential equations within Sobolev spaces, focusing on mild solutions and their qualitative properties.
Jianchao Bai, Jinxing Liu
doaj   +1 more source

Controllability results for semilinear functional and neutral functional evolution equations with infinite delay [PDF]

Surveys in Mathematics and its Applications, 2009
In this paper sufficient conditions are given ensuring the controllability of mild solutions defined on a bounded interval for two classes of first order semilinear functional and neutral functional differential equations involving evolution operators ...
Selma Baghli, Mouffak Benchohra, Khalil Ezzinbi   +2 more
doaj  

Conformable Fractional Cosine Families of Operators

Journal of Mathematical Sciences and Modelling, 2019
In this paper we are concerned with the problem \begin{eqnarray*}\begin{cases} u^{(\alpha)}(t)=Au(t)+f(t,u(t))& t\in [0,T]\\ u(0)=u_0, D^{\alpha}u(0)=u_1\end{cases}\end{eqnarray*}  \begin{eqnarray*}     \begin{cases}     u^{(\alpha)}(t)=Au(t)+f(t,u(t)
L. S. Chadli, Said Melliani, Elomari M'hamed   +2 more
doaj   +1 more source

Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay [PDF]

Opuscula Mathematica, 2014
In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces.
M. Mallika Arjunan, N. Y. Nadaf
doaj   +1 more source

New Outcomes Regarding the Existence of Hilfer Fractional Stochastic Differential Systems via Almost Sectorial Operators

Fractal and Fractional, 2022
In this paper, we focus on the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. The main results are obtained by using the concepts and ideas from fractional calculus, multivalued maps, semigroup theory ...
Sivajiganesan Sivasankar, Ramalingam Udhayakumar   +1 more
doaj   +1 more source

Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

Nonautonomous Dynamical Systems, 2020
In this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer.
Diop Mamadou Abdoul, Bete Kora Hafiz, Kakpo Reine, Ogouyandjou Carlos   +3 more
doaj   +1 more source

Controllability of Fractional Integro-Differential Equations with Delays and Singular Kernels in Fréchet Spaces

Mathematics
This paper is devoted to the investigation of existence and approximate controllability results for a class of fractional integro-differential equations formulated in Fréchet spaces.
Fatima Mesri, Abdelkrim Salim, Mouffak Benchohra   +2 more
doaj   +1 more source

Mild solutions for abstract fractional differential equations

Applicable Analysis, 2013
We propose a unified functional analytic approach to derive a variation of constants formula for a wide class of fractional differential equations using results on (a, k)-regularized families of bounded and linear operators, which covers as particular cases the theories of C 0-semigroups and cosine families.
Lizama, Carlos, N'Guerekata, Gaston M.
openaire   +3 more sources

The Existence and Uniqueness of Mild Solutions for Fuzzy Hilfer Fractional Evolution Equations with Non-Local Conditions

Axioms
In this paper, we investigate a fuzzy Hilfer fractional evolution equation of type ...
Kholoud N. Alharbi, Sanaa Alotaibi
doaj   +1 more source