scholarly journals Approximate controllability of fractional integro-differential equations involving nonlocal initial conditions

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
NI Mahmudov ◽  
S Zorlu
Keyword(s):  
Differential Equations ◽  
Approximate Controllability ◽  
Initial Conditions ◽  
Nonlocal Initial Conditions

SEMILINEAR NONLOCAL PROBLEMS WITHOUT THE ASSUMPTIONS OF COMPACTNESS IN BANACH SPACES

2010 ◽  
Vol 08 (02) ◽  
pp. 211-225 ◽  
Author(s):  
XINGMEI XUE
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Differential System ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Problems ◽  
Hausdorff Measure Of Noncompactness ◽  
Nonlocal Initial Conditions

In this paper, we study the semilinear differential equations with nonlocal initial conditions in the separable Banach spaces. We derive conditions expressed in terms of the Hausdorff measure of noncompactness under which the mild solutions exit. For illustration, a partial integral differential system is worked out.

scholarly journals Existence and regularity of mild solutions in some interpolation spaces for functional partial differential equations with nonlocal initial conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 113-126
Author(s):  
Xuping Zhang ◽  
Qiyu Chen ◽  
Yongxiang Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Linear Part ◽  
Fractional Power ◽  
Interpolation Spaces ◽  
Partial Differential ◽  
Nonlocal Initial Conditions ◽  
Spatial Derivatives

AbstractThis paper is devoted to study the existence and regularity of mild solutions in some interpolation spaces for a class of functional partial differential equations with nonlocal initial conditions. The linear part is assumed to be a sectorial operator in Banach space X. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. Moreover, we present an example to illustrate the application of main results.

Approximate controllability of fractional stochastic evolution equations with nonlocal conditions

2020 ◽  
Vol 21 (7-8) ◽  
pp. 829-841
Author(s):  
Yonghong Ding ◽  
Yongxiang Li
Keyword(s):  
Approximate Controllability ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Nonlocal Conditions ◽  
Nonlocal Term ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Approximation Techniques ◽  
Nonlocal Initial Conditions ◽  
The Fixed Point Theorem

AbstractThis paper deals with the approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We delete the compactness condition or Lipschitz condition for nonlocal term appearing in various literatures, and only need to suppose some weak growth condition on the nonlocal term. The discussion is based on the fixed point theorem, diagonal argument and approximation techniques. In the end, an example is presented to illustrate the abstract theory.

Sign in / Sign up

Export Citation Format

Share Document