Fast‐time complete controllability of nonlinear fractional delay integrodifferential evolution equations with nonlocal conditions and a parameter

2021 ◽  
Author(s):  
Daliang Zhao ◽  
Yansheng Liu ◽  
Haitao Li
Keyword(s):  
Evolution Equations ◽  
Nonlocal Conditions ◽  
Fast Time ◽  
Complete Controllability ◽  
Fractional Delay

Fractional evolution equations with nonlocal conditions in partially ordered Banach space

2018 ◽  
Vol 34 (3) ◽  
pp. 379-390
Author(s):  
HEMANT KUMAR NASHINE ◽  
◽  
HE YANG ◽  
RAVI P. AGARWAL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Coupled Fixed Point ◽  
Positive Cone ◽  
Bounded Linear ◽  
Partially Ordered ◽  
C0 Semigroup ◽  
Uniformly Bounded

In the present work, we discuss the existence of mild solutions for the initial value problem of fractional evolution equation of the form where C Dσ t denotes the Caputo fractional derivative of order σ ∈ (0, 1), −A : D(A) ⊂ X → X generates a positive C0-semigroup T(t)(t ≥ 0) of uniformly bounded linear operator in X, b > 0 is a constant, f is a given functions. For this, we use the concept of measure of noncompactness in partially ordered Banach spaces whose positive cone K is normal, and establish some basic fixed point results under the said concepts. In addition, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. We also supply some new coupled fixed point results via MNC. To justify the result, we prove an illustrative example that rational of the abstract results for fractional parabolic equations.

scholarly journals Complete controllability for a class of fractional evolution equations with uncertainty

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Nguyen Thi Kim Son ◽  
◽  
Nguyen Phuong Dong ◽  
Le Hoang Son ◽  
Alireza Khastan ◽  
...  
Keyword(s):  
Evolution Equations ◽  
Complete Controllability ◽  
Fractional Evolution Equations

A Study on Impulsive Hilfer Fractional Evolution Equations with Nonlocal Conditions

2020 ◽  
Vol 21 (2) ◽  
pp. 205-218
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fractional Derivative ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Sobolev Type ◽  
Initial Value ◽  
Liouville Fractional Derivative ◽  
Characteristic Solution Operators ◽  
Impulsive Evolution Equations

AbstractIn this paper, we concern with the existence of mild solution to nonlocal initial value problem for nonlinear Sobolev-type impulsive evolution equations with Hilfer fractional derivative which generalized the Riemann–Liouville fractional derivative. At first, we establish an equivalent integral equation for our main problem. Second, by means of the properties of Hilfer fractional calculus, combining measure of noncompactness with the fixed-point methods, we obtain the existence results of mild solutions with two new characteristic solution operators. The results we obtained are new and more general to known results. At last, an example is provided to illustrate the results.

Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2

2019 ◽  
Vol 22 (4) ◽  
pp. 1086-1112 ◽  
Author(s):  
Linxin Shu ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Approximate Controllability ◽  
Stochastic Systems ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Mönch Fixed Point Theorem ◽  
Liouville Derivative ◽  
Liouville Fractional Derivative

Abstract In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2. As far as we know, there are few articles investigating on this issue. Firstly, the mild solutions to the equations are proved using Laplace transform of the Riemann-Liouville derivative. Moreover, the estimations of resolve operators involving the Riemann-Liouville fractional derivative of order 1 < α < 2 are given. Then, the existence results are obtained via the noncompact measurement strategy and the Mönch fixed point theorem. The approximate controllability of this nonlinear Riemann-Liouville fractional nonlocal stochastic systems of order 1 < α < 2 is concerned under the assumption that the associated linear system is approximately controllable. Finally, the approximate controllability results are obtained by using Lebesgue dominated convergence theorem.

scholarly journals Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Fixed Point ◽  
Linear System ◽  
Fixed Point Theorem ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Complete Controllability ◽  
Approximately Controllable ◽  
Sobolev Type Differential Equations

We discuss the approximate controllability of semilinear fractional Sobolev-type differential system under the assumption that the corresponding linear system is approximately controllable. Using Schauder fixed point theorem, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional Sobolev-type differential equations, are formulated and proved. We show that our result has no analogue for the concept of complete controllability. The results of the paper are generalization and continuation of the recent results on this issue.

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