Abstract
This paper deals with complete controllability of systems governed by linear and semilinear conformable differential equations. By establishing conformable Gram criterion and rank criterion, we give sufficient and necessary conditions to examine that a linear conformable system is null completely controllable. Further, we apply Krasnoselskii’s fixed point theorem to derive a completely controllability result for a semilinear conformable system. Finally, three numerical examples are given to illustrate our theoretical results.
Highlights
Conformable calculus and equations has a rapid development in basic theory and application in many fields
Khan and Khan [9] concerned the open problem in Abdeljawad [1] and introduced the generalized conformable operators, which are the generalizations of Katugampola, Riemann–Liouville, and Hadamard fractional operators
Bendouma and Hammoudi [3] established the conformable dynamic equations on time scales with nonlinear functional boundary value conditions and obtained the existence
Summary
Conformable calculus and equations has a rapid development in basic theory and application in many fields. Bendouma and Hammoudi [3] established the conformable dynamic equations on time scales with nonlinear functional boundary value conditions and obtained the existence. Bohner and Hatipoglu [4] used conformable derivatives to establish thenew dynamic cobweb models and obtained the general solutions and stability criteria. Abdeljawad et al [2] proposed conformable quadratic and cubic logistic models and obtained existence theorems and stability of solutions. Jaiswal and Bahuguna [7] proposed conformable abstract Cauchy problems via semigroup theory, introduced the concept of mild and strong solution, and obtained existence and uniqueness theorem. Bouaouid et al [5] investigated nonlocal problems for second-order evolution differential equation in the frame of sequential conformable derivatives and presented Duhamel’s formula and existence, stability, and regularity of mild solutions. The corresponding control function is presented. (ii) We construct a suitable control function and apply Krasnoselskii’s fixed point to derive complete controllability of (2)
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