Abstract
In this paper, we will study a fractional initial value problem. By using Laplace transform, we obtain an equivalent fixed point problem, that is a Volterra integral equation involving the generalized Mittag-Leffler function in the kernel. The existence results are obtained by some fixed point theorems.
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Chidouh, A., Guezane-Lakoud, A. & Bebbouchi, R. Positive solutions for an oscillator fractional initial value problem. J. Appl. Math. Comput. 54, 57–68 (2017). https://doi.org/10.1007/s12190-016-0996-9
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DOI: https://doi.org/10.1007/s12190-016-0996-9
Keywords
- Fractional differential equations
- Volterra integral equation
- Initial value problem
- Laplace transform
- Mittag-Leffler function
- Fixed point theorem