scholarly journals Controllability for Sobolev type fractional integro-differential systems in a Banach space

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Hamdy M Ahmed
Keyword(s):  
Banach Space ◽  
Sobolev Type ◽  
Differential Systems

BLOW-UP PHENOMENA PROFILE FOR HADAMARD FRACTIONAL DIFFERENTIAL SYSTEMS IN FINITE TIME

Fractals ◽  
2019 ◽  
Vol 27 (06) ◽  
pp. 1950093 ◽  
Author(s):  
LI MA
Keyword(s):  
Banach Space ◽  
Lipschitz Condition ◽  
General Condition ◽  
Finite Time ◽  
Blow Up ◽  
Differential Systems ◽  
Functional Operator ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Theoretical Results

The main purpose of this paper is to investigate the weak singularity of solutions for some nonlinear Hadamard fractional differential systems (HFDSs). By constructing proper Banach space and employing lower and upper solutions technique, we prove the existence of the blow-up solutions for a class of HFDSs. In addition, we establish a more general condition than the classical Lipschitz condition which is employed to guarantee the equivalence between the solutions to HFDS and the corresponding functional operator. Also several examples are presented to verify our theoretical results.

EXISTENCE AND CONTROLLABILITY RESULTS FOR INFINITE DELAY PARTIAL FUNCTIONAL DIFFERENTIAL SYSTEMS WITH MULTI-VALUED IMPULSES IN BANACH SPACES

2010 ◽  
Vol 03 (04) ◽  
pp. 631-646 ◽  
Author(s):  
Hanwen Ning ◽  
Bing Liu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential

This paper is concerned with the existence and controllability of solutions for infinite delay functional differential systems with multi-valued impulses in Banach space. Sufficient conditions for the existence are obtained by using a fixed point theorem for multi-valued maps due to Dhage. An example is also given to illustrate our results.

Subordination principle for fractional diffusion-wave equations of Sobolev type

2020 ◽  
Vol 23 (2) ◽  
pp. 427-449
Author(s):  
Rodrigo Ponce
Keyword(s):  
Banach Space ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Wave Equations ◽  
Mild Solutions ◽  
Fractional Diffusion ◽  
Sobolev Type ◽  
Diffusion Wave ◽  
Fractional Differential ◽  
Resolvent Families

AbstractIn this paper we study subordination principles for fractional differential equations of Sobolev type in Banach space. With the help of the theory of Sobolev type resolvent families (known also as propagation family) as well as these subordination principles, we obtain the existence of mild solutions for this kind of equations. We study simultaneously the case 0 < α < 1 and 1 < α < 2 for the Caputo and Riemann-Liouville fractional derivatives.

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