scholarly journals EXISTENCE AND APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL EVOLUTION EQUATIONS IN BANACH SPACES

2021 ◽  
Vol 11 (6) ◽  
pp. 2895-2920
Author(s):  
Haide Gou ◽  
◽  
Yongxiang Li
Keyword(s):  
Banach Spaces ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Fractional Evolution Equations

scholarly journals Monotone Iterative Technique for Fractional Evolution Equations in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Jia Mu
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Initial Value ◽  
Fractional Evolution Equations ◽  
Monotone Iterative ◽  
Noncompactness Measure

We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations which provides computable monotone sequences that converge to the extremal solutions in a sector generated by upper and lower solutions. An example to illustrate the applications of the main results is given.

Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators

2020 ◽  
Vol 23 (1) ◽  
pp. 268-291 ◽  
Author(s):  
Pengyu Chen ◽  
Xuping Zhang ◽  
Yongxiang Li
Keyword(s):  
Resolvent Operator ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Control Function ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Resolvent Operators ◽  
Fractional Evolution Equations ◽  
Theoretical Results

AbstractIn this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introducing a new Green’s function and constructing a control function involving Gramian controllability operator. The discussions are based on Schauder’s fixed point theorem as well as the theory of α-order solution operator and α-order resolvent operator. An example is given to illustrate the feasibility of our theoretical results.

scholarly journals On the Approximate Controllability of Fractional Evolution Equations with Generalized Riemann-Liouville Fractional Derivative

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
N. I. Mahmudov ◽  
M. A. McKibben
Keyword(s):  
Fixed Point ◽  
Linear System ◽  
Fractional Derivative ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Semigroup Theory ◽  
Abstract Theory ◽  
Fractional Evolution Equations ◽  
Liouville Fractional Derivative ◽  
Approximately Controllable

We discuss the approximate controllability of fractional evolution equations involving generalized Riemann-Liouville fractional derivative. The results are obtained with the help of the theory of fractional calculus, semigroup theory, and the Schauder fixed point theorem under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the abstract theory.

Sign in / Sign up

Export Citation Format

Share Document