Geodesic
A new result for fractional differential equation with nonlocal initial value using Caputo-Fabrizio derivative
Filomat, Tome 36 (2022) no. 9, p. 2881

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DOI

In this paper, using Caputo-Fabrizio fractional derivative, we obtain some new results for the existence and uniqueness of solutions of differential equation with nonlocal initial value about fractional order 0 α 1. These results are applied with the help of Arzela-Ascoli theorem and Schauder fixed point. Also based on some α-contractive maps for such problems, some new unique theorem has been introduced and proved. Finally, some illustrative example is considered to show the effectiveness of the results.
DOI : 10.2298/FIL2209881M
Classification : 35R11, 45E10, 34A08
Keywords: Fractional differential equations, Caputo-Fabrizio derivative, Nonlocal condition, Fixed point 
Z Mokhtary; M B Ghaemi; S Salahshour. A new result for fractional differential equation with nonlocal initial value using Caputo-Fabrizio derivative. Filomat, Tome 36 (2022) no. 9, p. 2881 . doi: 10.2298/FIL2209881M
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     author = {Z Mokhtary and M B Ghaemi and S Salahshour},
     title = {A new result for fractional differential equation with nonlocal initial value using {Caputo-Fabrizio} derivative},
     journal = {Filomat},
     pages = {2881 },
     year = {2022},
     volume = {36},
     number = {9},
     doi = {10.2298/FIL2209881M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2209881M/}
}
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