WITHDRAWN: On controllability of fractional evolution nonlocal Cauchy problem in Banach spaces

2011 ◽  
Author(s):  
Shuxian Lun ◽  
Zhixin Tai
Keyword(s):  
Cauchy Problem ◽  
Banach Spaces ◽  
Nonlocal Cauchy Problem

scholarly journals EXISTENCE OF SOLUTIONS OF SEMILINEAR DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS IN BANACH SPACES

1999 ◽  
Vol 30 (1) ◽  
pp. 21-28
Author(s):  
K. BALACHANDR AN ◽  
M. CHANDRASEKARAN
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Banach Spaces ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Global Solutions ◽  
Contraction Mapping Principle ◽  
Analytic Semigroups ◽  
Nonlocal Cauchy Problem

The aim of this paper is to prove the existence and uniquencess of local, strong and global solutions of a nonlocal Cauchy problem for a differential equation. The method of analytic semigroups and the contraction mapping principle arc used to establish the results.

scholarly journals An Application Of The Theory Of Scale Of Banach Spaces

2015 ◽  
Vol 29 (1) ◽  
pp. 51-59
Author(s):  
Łukasz Dawidowski
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Banach Spaces ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Scale Of Banach Spaces ◽  
The Cauchy Problem ◽  
Selection Of

AbstractThe abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity of the solutions.

scholarly journals Uniqueness criterion for solution of abstract nonlocal Cauchy problem

1993 ◽  
Vol 6 (1) ◽  
pp. 49-54 ◽  
Author(s):  
L. Byszewski
Keyword(s):  
Cauchy Problem ◽  
Nonlocal Condition ◽  
Nonlocal Problem ◽  
Dissipative Operator ◽  
Uniqueness Criterion ◽  
Nonlocal Cauchy Problem

The aim of the paper is to prove an uniqueness criterion for a solution of an abstract nonlocal Cauchy problem. A dissipative operator in the nonlocal problem and an arbitrary functional in the nonlocal condition are considered. The paper is a continuation of papers [1]-[3] and generalizes some results from [4].

scholarly journals Existence of approximate solution to abstract nonlocal Cauchy problem

1992 ◽  
Vol 5 (4) ◽  
pp. 363-373 ◽  
Author(s):  
L. Byszewski
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Approximate Solution ◽  
Closed Subset ◽  
Nonlocal Condition ◽  
Right Hand ◽  
The Right ◽  
Nonlocal Cauchy Problem

The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3].

scholarly journals Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces

2019 ◽  
Vol 3 (2) ◽  
pp. 27 ◽  
Author(s):  
Ayşegül Keten ◽  
Mehmet Yavuz ◽  
Dumitru Baleanu
Keyword(s):  
Banach Spaces ◽  
Fractional Derivatives ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Kernel Functions ◽  
Banach Contraction ◽  
Exponential Decay Law ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

We investigated existence and uniqueness conditions of solutions of a nonlinear differential equation containing the Caputo–Fabrizio operator in Banach spaces. The mentioned derivative has been proposed by using the exponential decay law and hence it removed the computational complexities arising from the singular kernel functions inherit in the conventional fractional derivatives. The method used in this study is based on the Banach contraction mapping principle. Moreover, we gave a numerical example which shows the applicability of the obtained results.

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