Existence of solutions for a fractional hybrid boundary value problem via measures of noncompactness in Banach algebras
Keywords
Banach algebras, Riemann-Liouville fractional derivative, measure of noncompactness, hybrid boundary value problemAbstract
We study the existence of solutions for the following fractional hybrid boundary value problem $$ \cases \displaystyle D_{0^+}^{\alpha}\bigg[\frac{x(t)}{f(t,x(t))}\bigg]+g(t,x(t))=0, &0< t< 1,\\ x(0)=x(1)=0, \endcases $$ where $1< \alpha\leq 2$ and $D_{0^+}^{\alpha}$ denotes the Riemann-Liouville fractional derivative. The main tool is our study is the technique of measures of noncompactness in the Banach algebras. Some examples are presented to illustrate our results. Finally, we compare the results of paper with the ones obtained by other authors.Downloads
Published
2016-04-12
How to Cite
1.
CABALLERO, Josefa, DARWISH, Mohamed Abdalla and SADARANGANI, Kishin. Existence of solutions for a fractional hybrid boundary value problem via measures of noncompactness in Banach algebras. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 43, no. 2, pp. 535 - 548. [Accessed 24 April 2024].
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