Đang chuẩn bị liên kết để tải về tài liệu:
Hyers-Ulam stability for nonlocal differential equations

Không đóng trình duyệt đến khi xuất hiện nút TẢI XUỐNG

In this paper, we present a result on Hyers-Ulam stability for a class of nonlocal differential equations in Hilbert spaces by using the theory of integral equations with completely positive kernels together with a new Gronwall inequality type. The paper develops some recent results on fractional differential equations to the ones involving general nonlocal derivatives. Instead of Mittag-Leffler functions, we must utilize the characterization of relaxation function. | HNUE JOURNAL OF SCIENCE DOI 10.18173 2354-1059.2020-0041 Natural Science 2020 Volume 65 Issue 10 pp. 3-9 This paper is available online at http stdb.hnue.edu.vn HYERS-ULAM STABILITY FOR NONLOCAL DIFFERENTIAL EQUATIONS Nguyen Van Dac1 and Pham Anh Toan2 1 Faculty of Computer Science and Engineering Thuyloi University 2 Nguyen Thi Minh Khai High School Hanoi Abstract. In this paper we present a result on Hyers-Ulam stability for a class of nonlocal differential equations in Hilbert spaces by using the theory of integral equations with completely positive kernels together with a new Gronwall inequality type. The paper develops some recent results on fractional differential equations to the ones involving general nonlocal derivatives. Instead of Mittag-Leffler functions we must utilize the characterization of relaxation function. Keywords nonlocal differential equation mild solution Hyers-Ulam stability. 1. Introduction Let H be a separable Hilbert space. Consider the following equation k t u t Au t f t u t t J 0 T . 1.1 where the unknown function u takes values in H the kernel k L1loc R A is an inbounded linear operator and f J H H is a Rgiven function. Here the t notation denotes the Laplace convolution i.e. k v t 0 k t s v s ds. In 1 authors introduced a result on the existence regularity and stability for mild solutions to 1.1 where f depends only on u and the initial condition is given by u 0 u0 . 1.2 Our goal in this paper is to consider the Hyers-Ulam stability for 1.1 . The Hyers-Ulam stability for functional equations was founded in 1940 by S.M Ulam in a talk at Wisconsin University see 2 and by D. H Hyers answer a year later for additive functions defined on Banach spaces see 3 . However the first result on the Hyers-Ulam stability of a differential equation was addressed by C.Alsina and R. Ger in 1998 see 4 . In this remarkable work they proved that if a differentiable function Received October 2 2020. Revised October 23 2020. Accepted October 30 2020. .

TÀI LIỆU LIÊN QUAN
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.