# Nonnegative solution for singular nonlinear fractional differential equation with coefficient that changes sign

Nonnegative solution for singular nonlinear fractional differential equation with coefficient... In this paper, we consider the existence of nonnegative solutions of initial value problem for singular nonlinear fractional differential equation $$D^{s} u(t)=\lambda a(t)f(u, D^{\alpha} u), u(0) = 0, 0 < t \leq 1, 0 < \alpha < s < 1$$ where D s and D α are the standard Riemann-Liouville fractional derivatives, $$f : [0,\infty) \times (-\infty,+\infty) \rightarrow [0,+\infty), a : (0,1] \rightarrow R$$ , may be change sign, t r a : [0,1] → R, 0 ≤ r < s − α, and λ > 0 is a parameter. Our analysis relies on the Schauder fixed point theorem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Nonnegative solution for singular nonlinear fractional differential equation with coefficient that changes sign

, Volume 12 (4) – Oct 4, 2008
14 pages

/lp/springer_journal/nonnegative-solution-for-singular-nonlinear-fractional-differential-eu6We9g5SH
Publisher
SP Birkhäuser Verlag Basel
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2030-4
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we consider the existence of nonnegative solutions of initial value problem for singular nonlinear fractional differential equation $$D^{s} u(t)=\lambda a(t)f(u, D^{\alpha} u), u(0) = 0, 0 < t \leq 1, 0 < \alpha < s < 1$$ where D s and D α are the standard Riemann-Liouville fractional derivatives, $$f : [0,\infty) \times (-\infty,+\infty) \rightarrow [0,+\infty), a : (0,1] \rightarrow R$$ , may be change sign, t r a : [0,1] → R, 0 ≤ r < s − α, and λ > 0 is a parameter. Our analysis relies on the Schauder fixed point theorem.

### Journal

PositivitySpringer Journals

Published: Oct 4, 2008

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