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Baleanu, Dumitru,Arjunan, Mani Mallika,Nagaraj, Mahalingam,Suganya, Selvaraj Korean Mathematical Society 2018 대한수학회보 Vol.55 No.4
This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.
Dumitru Baleanu,Mani Mallika Arjunan,Mahalingam Nagaraj,Selvaraj Suganya 대한수학회 2018 대한수학회보 Vol.55 No.4
This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.
HYERS-ULAM STABILITY OF FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH RANDOM IMPULSE
Dumitru Baleanu,Banupriya Kandasamy,Ramkumar Kasinathan,Ravikumar Kasinathan,Varshini Sandrasekaran Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.3
The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.
Effect of microtemperatures for micropolar thermoelastic bodies
Marin Marin,Dumitru Baleanu,Sorin Vlase 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.61 No.3
In this paper we investigate the theory of micropolar thermoelastic bodies whose micro-particles possess microtemperatures. We transform the mixed initial boundary value problem into a temporally evolutionary equation on a Hilbert space and after that we prove the existence and uniqueness of the solution. We also approach the study of the continuous dependence of solution upon initial data and loads.
Optimal Control of a MIMO Bioreactor System Using Direct Approach
Abolfazl Simorgh,Abolhassan Razminia,Saleh Mobayen,Dumitru Baleanu 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.3
In this paper, the optimal control of a continuous type bioreactor with multi-input-multi-output signals is presented for the two active phases: growth and stationary. The underlying criterion to be minimized generalizes the classic quadratic forms to address some crucial objectives in controlling the bioreactor. In particular, the protection of actuators against fast switching in the controller output is considered by including a weighting term of the control signal derivatives. The direct optimal control approach is used to carry out the optimization in the presenceof various limiting constraints. Direct methods are based on transcribing the infinite-dimensional problem to a finite-dimensional one. In this manuscript, direct single shooting and trapezoidal collocation methods are used for transcription, and the successive quadratic programming method is employed to solve the resulting nonlinear programming problem. It is shown that the trapezoidal method is an effective method for controlling the bioreactor in all the active phases, whereas the single shooting fails in dealing with the unstable one (i.e., growth). To analyzesolutions in a more accurate manner, an auxiliary criterion is defined, and then the cheap control analysis is studied. The convergence to the lowest value of the auxiliary cost function and the effects on the optimal state and control trajectories are then examined by varying cheap parameters. Several numerical simulations support the presented theoretical formulation.