Affiliation:
1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Kogălniceanu Str., no. 1, Cluj-Napoca, 400084, Romania
Abstract
Abstract
The purpose of the paper is to investigate the global existence of solutions to initial value problems for nonlinear fractional differential equations on the semi-axis. More precisely, it deals with the initial value problem (*)$\left\{ \begin{gathered}
D_{0 + }^\alpha x(t) = f(t,x(t)),t \in [0,\infty ], \hfill \\
\lim _{t \to 0 + } t^{1 - \alpha } x(t) = x_0 , \hfill \\
\end{gathered} \right.
$ where 0 < α < 1, D
0+α denotes the Riemann-Liouville fractional derivative of order α, and f: (0,∞) × ℝ → ℝ is a continuous function. Unlike all the previous papers dealing with the problem of existence of solutions to (*), this problem is solved here by constructing a special locally convex space which is metrizable and complete. Then Schauder’s fixed point theorem enables to provide sufficient conditions on f, ensuring that (*) possesses at least one solution. The growth conditions imposed to f are weaker than other similar conditions already used in the literature.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Cited by
17 articles.
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