China
Africa
Explore chapters and articles related to this topic
Controllability on Non-dense Delay Fractional Differential System with Non-Local Conditions
Published in Harendra Singh, Devendra Kumar, Dumitru Baleanu, Methods of Mathematical Modelling, 2019
C. Ravichandran, K. Jothimani, Devendra Kumar
This article illustrates that the controllability results on fractional integrodifferential system with delay behaviour is non-densely defined on Banach space using the fractional calculus, measure of non-compactness and Monch fixed point theorem. Our theorem guarantees the effectiveness of controllability, which is the result of the system concerned. It would be interesting if we investigate the same in Hilbert space by employing some other fixed point theorems that are suitable to the nature of the system. Moreover, we can explore the optimal controllability for various types of fractional integro-differential equations. It has many significant applications not only in control theory and systems theory but also in such fields as industrial and chemical process control, reactor control and control of electric bulk power systems, medical sciences, aerospace engineering and recently in quantum systems theory. In particular, the non-linear fractional integro-differential equation is implemented for the ECG images to detect the abnormal heart rates of the patient.
On uniform regularity and strong regularity
Published in Optimization, 2018
R. Cibulka, J. Preininger, T. Roubal
Note that (ii) in Theorem 2.6 is satisfied, in particular, when σ has a point-based approximation on Ω in the sense of Robinson [6]. Theorem 2.6 yields [5, Lemma 0]. Moreover, given a non-empty subset Ω of a metric space, define the measure of non-compactness of Ω by Then Theorem 2.6 holds provided that is strictly smaller than the infimum of the reciprocal values of the regularity moduli of the mappings appearing in (i). This statement is a key element in the proof of the non-smooth versions of Robinson and Lyusternik-Graves theorems, cf. [1, Step 1] and [2, Lemma 12].
Non-instantaneous impulsive Hilfer–Katugampola fractional stochastic differential equations with fractional Brownian motion and Poisson jumps
Published in Journal of Control and Decision, 2023
A. M. Sayed Ahmed, Hamdy M. Ahmed
The Hausdorff measure of non-compactness (MNC) defined on each bounded subset Υ of the Banach space is given by equal infimum of such that Υ can be covered by finite number of balls with radii ε.