Geodesic
Weighted fractional neutral functional differential equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 5, pp. 535-549

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In this paper, we consider a weighted neutral functional differential equation of fractional order $0\alpha 1$, with nonzero initial values, infinite delay, and the standard Riemann–Liouville fractional derivative. By using a variety of tools of fractional calculus including the Schauder fixed point theorem and the Banach fixed point theorem, we verify the existence, uniqueness and continuous dependence of solution of weighted neutral problem.
Keywords: fractional functional differential equations, fractional derivative and fractional integral, existence and continuous dependence, fixed point theorem. 
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     author = {Mohammed S. Abdo and Satish K. Panchal},
     title = {Weighted fractional neutral functional differential equations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {535--549},
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     number = {5},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_5_a0/}
}
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Mohammed S. Abdo; Satish K. Panchal. Weighted fractional neutral functional differential equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 5, pp. 535-549. http://geodesic.mathdoc.fr/item/JSFU_2018_11_5_a0/