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Journal of Applied Mathematics and Computing

Erschienen in:

01.06.2016 | Original Research

Cauchy problem for nonlinear fractional differential equations with positive constant coefficient

verfasst von: Shan Peng, JinRong Wang

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2016

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Abstract

In this paper, we consider a Cauchy problem for nonlinear fractional differential equation with constant coefficient \(\lambda >0\) of the type: \( ^{c} D_{t}^{\alpha }x(t)=\lambda x(t)+f(t,x(t))\) with \(x(0)=x_{0}\). We present monotonicity and continuity of two-parameter Mittag-Leffler function \({\mathbb {E}}_{\alpha ,\beta }(z)\) for \(z>0\). By using monotonicity, continuity, asymptotic properties of \({\mathbb {E}}_{\alpha ,\beta }(z)\) for \(z>0\) and fixed point theorems, we obtain existence of solution. Finally, two examples are given to illustrate our theoretical results.

Vorheriger Artikel Boundary control of nonlinear elastic systems

Nächster Artikel Morse theory and local linking for a class of boundary value problems with impulsive effects

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Titel: Cauchy problem for nonlinear fractional differential equations with positive constant coefficient
verfasst von: Shan Peng
JinRong Wang
Publikationsdatum: 01.06.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2016
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-015-0908-4

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