Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Ulam-Hyers Stability Results For A Novel Nonlinear Nabla Caputo Fractional Variable-Order Difference System, Danfeng Luo, Thabet Abdeljawad, Zhiguo Luo
Ulam-Hyers Stability Results For A Novel Nonlinear Nabla Caputo Fractional Variable-Order Difference System, Danfeng Luo, Thabet Abdeljawad, Zhiguo Luo
Turkish Journal of Mathematics
This paper is concerned with a kind of nonlinear Nabla Caputo fractional difference system with variable-order and fixed initial valuable. By applying Krasnoselskii's fixed point theorem, we give some sufficient conditions to guarantee the existence results for the considered fractional discrete equations. In addition, we further consider the Ulam-Hyers stability by means of generalized Gronwall inequality. At last, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.
Rotating Periodic Integrable Solutions For Second-Order Differential Systems With Nonresonance Condition, Yi Cheng, Ke Jin, Ravi Agarwal
Rotating Periodic Integrable Solutions For Second-Order Differential Systems With Nonresonance Condition, Yi Cheng, Ke Jin, Ravi Agarwal
Turkish Journal of Mathematics
In this paper, by using Parseval's formula and Schauder's fixed point theorem, we prove the existence and uniqueness of rotating periodic integrable solution of the second-order system $x''+f(t,x)=0$ with $x(t+T)=Qx(t)$ and $\int_{(k-1)T}^{kT}x(s)ds=0$, $k\in Z^+$ for any orthogonal matrix $Q$ when the nonlinearity $f$ satisfies nonresonance condition.
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the Leray-Schauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).