A singular boundary value problem for nonlinear differential equations of fractional order |
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Authors: | Nickolai Kosmatov |
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Institution: | 1. Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR, 72204-1099, USA
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Abstract: | We are concerned with the nonlinear differential equation of fractional order $$\mathcal{D}^{\alpha}_{0+}u(t)=f(t,u(t),u'(t)),\quad \mbox{a.\,e.}\ t\in (0,1),$$ where $\mathcal{D}^{\alpha}_{0+}$ is the Riemann-Liouville fractional order derivative, subject to the boundary conditions $$u(0)=u(1)=0.$$ We obtain the existence of at least one solution using the Leray-Schauder Continuation Principle. |
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