Abstract
This paper investigates the optimal control for a class of nonlocal fractional evolution equations of order gamma in (1,2) in Banach spaces. An adequate definition of α-mild solutions is obtained and the existence, uniqueness and continuous dependence of α-mild solutions for the presented control system are also established. The existence of optimal pairs of nonlocal fractional evolution systems is also demonstrated with a view on the construction of the Lagrange problem. Finally, an example is propounded for the presentation of optimal control.
Highlights
Applied linguistic mathematics has the sub-branch of the theory of fractional differential equations
We investigate the optimal control for the fractional evolution system (1) with nonlocal conditions
4 Continuous dependence we show that the mild solution of the system (1) shows a continuous dependence on the initial value with respect to the control term
Summary
Applied linguistic mathematics has the sub-branch of the theory of fractional differential equations. Based on the concept of the sectorial operator, Shu [11] minutely studied the existence and uniqueness of mild solutions for nonlocal fractional differential equations. Very recent studies with new results on the controllability of fractional evolution systems with order γ ∈ (1, 2) have been presented in [27,28,29,30,31]. The industrial sterilization of canned foods is a process in which there usually occurs a degradation of nutrients and a deterioration of qualitative properties due to the temperature to which the food is overexposed in order to ensure destroying pathogenic microorganisms We face this problem using optimal control methods. An example is propounded for the presentation of optimal control
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
