An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative
| Autor: | Hamidreza Marasi, Hassen Aydi, A. Soltani Joujehi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Picard–Lindelöf theorem
Article Subject 010102 general mathematics Derivative 01 natural sciences Fractional calculus law.invention Kernel (algebra) Invertible matrix law 0103 physical sciences QA1-939 Shaping Applied mathematics Initial value problem 0101 mathematics 010306 general physics Analysis Picard theorem Mathematics |
| Zdroj: | Journal of Function Spaces, Vol 2021 (2021) |
| ISSN: | 2314-8888 2314-8896 |
| Popis: | In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution. |
| Databáze: | OpenAIRE |
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