Geodesic
New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative
Communications in Mathematics, Tome 27 (2019) no. 2, pp. 113-141.

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In this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel'skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness of our main results.
Classification : 34A08, 34A37, 47H10
Keywords: Fractional differential equations; Boundary value problems; Erdélyi-Kober derivative; Fixed point theorems; Existence; Uniqueness. 
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     author = {Arioua, Yacine and Titraoui, Maria},
     title = {New class of boundary value problem for nonlinear fractional differential equations involving {Erd\'elyi-Kober} derivative},
     journal = {Communications in Mathematics},
     pages = {113--141},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2019},
     mrnumber = {4058170},
     zbl = {1464.34016},
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     url = {http://geodesic.mathdoc.fr/item/COMIM_2019__27_2_a4/}
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Arioua, Yacine; Titraoui, Maria. New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative. Communications in Mathematics, Tome 27 (2019) no. 2, pp. 113-141. http://geodesic.mathdoc.fr/item/COMIM_2019__27_2_a4/