Journal ArticleDOI
Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space
TLDR
In this article, the authors give a theorem about the existence and uniqueness of a solution of a nonlocal Cauchy problem for an ordinary differential equation in a Banach space.Abstract:
The aim of the paper is to give a theorem about the existence and uniqueness of a solution of a nonlocal Cauchy problem for an ordinary differential equation in a Banach space. The Banach theorem about the fixed point is used to prove the existence and uniqueness of a solution of the problem considered. The result obtained in this paper can be applied among other things to the description of motion phenomena with better effect than the classical Cauchy problem.read more
Citations
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Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem
TL;DR: In this article, the authors give three theorems about the existence and uniqueness of mild, strong, and classical solutions of a nonlocal Cauchy problem for a semilinear evolution equation.
Journal ArticleDOI
A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions
TL;DR: In this article, sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problems for fractional differential equations and inclusions involving the Caputo fractional derivative are established.
Journal ArticleDOI
Existence of mild solutions for fractional neutral evolution equations
Yong Zhou,Feng Jiao +1 more
TL;DR: By using the fractional power of operators and some fixed point theorems, a class of fractional neutral evolution equations with non local conditions with nonlocal conditions is discussed and various criteria on the existence and uniqueness of mild solutions are obtained.
Journal ArticleDOI
Nonlocal Cauchy problem for fractional evolution equations
Yong Zhou,Feng Jiao +1 more
TL;DR: In this paper, the nonlocal Cauchy problem is discussed for the fractional evolution equations in an arbitrary Banach space and various criteria on the existence and uniqueness of mild solutions are obtained.
Journal ArticleDOI
Boundary value problems for differential equations with fractional order and nonlocal conditions
TL;DR: In this article, sufficient conditions for the existence of solutions for a class of boundary value problems for fractional differential equations involving the Caputo fractional derivative and non-local conditions were established.
References
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Book
Nonlinear differential equations in abstract spaces
V. Lakshmikantham,S. Leela +1 more
TL;DR: In this article, the Cauchy problem has been studied in the context of the convergence of difference approximations in weak topology problems, where the exponential formula is used.
Journal ArticleDOI
Theorem about existence and uniqueness of continuous solution of nonlocal problem for nonlinear hyperbolic equation
TL;DR: In this paper, the authors give a theorem about the existence and uniqueness of the continuous solution of a non-linear differential hyperbolic problem with a nonlocal condition in a bounded domain.
Journal ArticleDOI
Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation uxt=F(x,t,u,ux)
TL;DR: In this article, the authors give two theorems about existence and uniqueness of continuous solutions for hyperbolic nonlinear differential problems with nonlocal conditions in bounded and unbounded domains.