Theoretical study of a \(\varphi \)-Hilfer fractional differential system in Banach spaces. (English) Zbl 07926147
Summary: In this work, we study the existence of solutions of nonlinear fractional coupled system of \(\varphi \)-Hilfer type in the frame of Banach spaces. We improve a property of a measure of noncompactness in a suitably selected Banach space. Darbo’s fixed point theorem is applied to obtain a new existence result. Finally, the validity of our result is illustrated through an example.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
Keywords:
\( \varphi \)-Hilfer fractional derivative; coupled system; fixed point; measure of noncompactnessReferences:
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