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Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay [PDF]

Journal of Inequalities and Applications, 2017
In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative. The definition of mild solutions for the
Haide Gou, Baolin Li
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Topological Structure of the Solution Sets for Impulsive Fractional Neutral Differential Inclusions with Delay and Generated by a Non-Compact Demi Group

Fractal and Fractional, 2022
In this paper, we give an affirmative answer to a question about the sufficient conditions which ensure that the set of mild solutions for a fractional impulsive neutral differential inclusion with state-dependent delay, generated by a non-compact semi ...
Zainab Alsheekhhussain, Ahmed Gamal Ibrahim, Akbar Ali   +2 more
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Results on Neutral Partial Integrodifferential Equations Using Monch-Krasnosel’Skii Fixed Point Theorem with Nonlocal Conditions

Fractal and Fractional, 2022
In this theory, the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch–Krasnosel’skii type of fixed point theorem, a measure of noncompactness
Chokkalingam Ravichandran, Kasilingam Munusamy, Kottakkaran Sooppy Nisar, Natarajan Valliammal   +3 more
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Mild Solutions for Impulsive Integro-Differential Equations Involving Hilfer Fractional Derivative with almost Sectorial Operators

Axioms, 2021
In this manuscript, we establish the mild solutions for Hilfer fractional derivative integro-differential equations involving jump conditions and almost sectorial operator. For this purpose, we identify the suitable definition of a mild solution for this
Kulandhaivel Karthikeyan, Panjaiyan Karthikeyan, Nichaphat Patanarapeelert, Thanin Sitthiwirattham   +3 more
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An Investigation on the Optimal Control for Hilfer Fractional Neutral Stochastic Integrodifferential Systems with Infinite Delay

Fractal and Fractional, 2022
The main concern of this manuscript is to study the optimal control problem for Hilfer fractional neutral stochastic integrodifferential systems with infinite delay.
Murugesan Johnson, Velusamy Vijayakumar
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Mild solutions for semilinear fractional differential equations

Electronic Journal of Differential Equations, 2009
This paper concerns the existence of mild solutions for fractional semilinear differential equation with non local conditions in the $alpha$-norm.
Gisele M. Mophou, Gaston M. N'Guerekata
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A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions [PDF]

Opuscula Mathematica, 2011
In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type: \[\begin{aligned}D_{t}^{q}x(t)&=Ax(t)+\int\limits_{0}^{t}B(t-s)x(s)ds+t^{n}f\left(t,x(t)\right),&&t\in [0,T],\;n\in Z^{+},
JinRong Wang, X. Yan, X.-H. Zhang, T.-M. Wang, X.-Z. Li   +4 more
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Mild Solutions of Quantum Stochastic Differential Equations [PDF]

Electronic Communications in Probability, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
FAGNOLA, FRANCO, WILLS S. J.
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Global mild solutions of Navier‐Stokes equations [PDF]

Communications on Pure and Applied Mathematics, 2011
AbstractWe establish a global well‐posedness of mild solutions to the three‐dimensional, incompressible Navier‐Stokes equations if the initial data are in the space ${\cal{X}}^{-1}$ defined by \input amssym ${\cal{X}}^{‐1} = \{f \in {\cal{D}}^\prime(R^3): \int_{{\Bbb{R}}^3}|\xi|^{‐1}|\widehat{f}|d\xi < \infty\}$ and if the norms of the initial data ...
Lei, Zhen, Lin, Fang-Hua
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Impulsive functional differential inclusions of mixed type with finite delay

上海师范大学学报. 自然科学版, 2020
In this paper, using fixed point theorem for multi-valued maps, we obtain the existence result of mild solutions for a class of impulsive functional differential inclusions of mixed type with finite delay.
LI Xiaoyue, WANG Qi
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