Abstract
In this paper, we investigate a class of impulsive Katugampola fractional differential equations with nonlocal conditions in a Banach space. First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. Secondly, we derive the sufficient conditions for optimal controls by building approximating minimizing sequences of functions twice.
Highlights
In recent years, fractional calculus has received more and more attention in many fields because of the local limit definition of integral-order ordinary differential equation or partial differential equation which is not suitable to describe the history-dependent process and has received more and more attention in many fields
Because fractional-order differential equation can describe objective laws and the essence of things more accurately than integral differential equation, many scholars have devoted themselves to the study of fractional calculus
Fractional differential equations are widely used in practice and greatly enriched the content of mathematical theory and penetrated into many fields of natural science
Summary
Fractional calculus has received more and more attention in many fields because of the local limit definition of integral-order ordinary differential equation or partial differential equation which is not suitable to describe the history-dependent process and has received more and more attention in many fields. When a parameter was fixed at different values, it produces the above integrals as special cases; when ρ ⟶ 1, we can get the RiemannLiouville operators; when ρ ⟶ 0, we can get the Hadamard operators (see [2]) He presented two representations of the generalized derivative called Katugampola derivative in [3]. In [4], he obtained existence and uniqueness results to the solution of initial value problem for a class of generalized fractional differential equations. Sun et al [35] considered a class of impulsive fractional differential equations with RiemannLiouville fractional derivative, the existence of solution was proved by using Darbo-Sadovskii's fixed-point theorem, and the optimal control results were obtained.
Sign-in/Register to view highlights & summary 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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
