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A singular boundary value problem for nonlinear differential equations of fractional order

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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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Correspondence to Nickolai Kosmatov.

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Kosmatov, N. A singular boundary value problem for nonlinear differential equations of fractional order. J. Appl. Math. Comput. 29, 125–135 (2009). https://doi.org/10.1007/s12190-008-0104-x

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  • DOI: https://doi.org/10.1007/s12190-008-0104-x

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