In this article, the existence and uniqueness of generalized nonlinear impulsive evolution equation is derived. The proposed system is modeled with nonlinear perturbed force which changes after every impulse. The Banach contraction principle is applied to prove the existence and uniqueness of mild solution. The existence and uniqueness of classical solution is obtained by fixing the impulse and the conditions in which mild solution becomes classical solution also obtained. Finally an example is illustrated to the effectiveness of main results.
Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.
In this manuscript, we have established conditions for the existence and uniqueness of mild and classical solutions to the fractional order Cauchy problem by including and without including impulses over the completed norm linear space (Banach space). Conditions are established using the concept of generators and the generalised Banach fixed point theorem, which are weaker conditions than the previously derived conditions. We have also established the conditions under which a mild solution to the problem gives rise to a classical solution to the given problem. Finally, illustrations of the existence and uniqueness of the solution are provided to validate our derived results.
In this manuscript, we have considered the system governed by a non-instantaneous impulsive dynamical system of integer ordered with classical and non-local conditions and derived sufficient conditions for the trajectory controllability of the system on the Banach space. The conditions were obtained through the concept of semi-group properties of operators and Gronwall's inequality. Finally, illustrations with the classical and non-local conditions were also added to validate the derived conditions.
In this article we have studied the controllability of artificial satellite under the effect of zonal harmonic J 2 in cylindrical polar coordinates systems. Seven different cases of thrusters in various directions have been analyzed and it is found that the system is controllable if we apply thrusters in either r, θ and z or θ and z direction. The equations governing motion of satellite have been linearized and Kalman controllability test is applied to check the controllability of the system. We have also derived controller u for the linearized system. The trajectory of the system have been plotted to show the controllability of the system.
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