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Journal of Applied Mathematics and Computing

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26.07.2016 | Original Research

Existence results to positive solutions of fractional BVP with ${\varvec{q}}$-derivatives

verfasst von: Rahmat Darzi, Bahram Agheli

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2017

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This paper investigates the existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem with fractional q-derivative

$$\begin{aligned}&D_{q}^{\alpha }u(t)+f(t,u(t))=0, \quad {0<t<1, ~3<\alpha \le 4,} \\&u(0)= D_{q}u(0)=D_{q}^{2}u(0)=0, \quad D_{q}^{2}u(1)=\beta D_{q}^{2}u(\eta ), \end{aligned}$$

where $D_{q}^{\alpha }$ denotes the Riemann–Liouville q-derivative of order $\alpha $, $0<\eta <1$ and $1-\beta \eta ^{\alpha -3}>0$. Our analysis relies a fixed point theorem in partially ordered sets. An example to illustrate our results is given.

Vorheriger Artikel Finite time stability analysis of systems based on delayed exponential matrix

Nächster Artikel Intuitionistic fuzzy soft graphs with applications

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Titel: Existence results to positive solutions of fractional BVP with -derivatives
verfasst von: Rahmat Darzi
Bahram Agheli
Publikationsdatum: 26.07.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2017
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-016-1040-9

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