Abstract
We discuss solvability of a nonlinear Riemann-Liouville integral equation in Lebesgue spaces. We treat the Volterra equations of the first and the second types by applying boundedness criteria for the Riemann-Liouville integral operator. The existence of a solution to integral equations will follow from the Leray-Schauder Nonlinear Alternative.
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Kosmatov, N. Integral equations of fractional order in Lebesgue spaces. FCAA 19, 665–675 (2016). https://doi.org/10.1515/fca-2016-0035
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DOI: https://doi.org/10.1515/fca-2016-0035
Key Words and Phrases
- Carathéodory conditions
- Leray-Schauder Nonlinear Alternative
- Riemann-Liouville derivative
- Volterra integral equation