Geodesic
A Global Existence and Uniqueness Theorem for Ordinary Differential Equations of Generalized Order
Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 267-271

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DOI

We extend the Picard's theorem to ordinary differential equation of generalized order α, 0 ≤ α ≤ l, and prove a global existence and uniqueness theorem by using the Banach contraction principle. 
Al-Abedeen, Ahmed Z.; Arora, H. L. A Global Existence and Uniqueness Theorem for Ordinary Differential Equations of Generalized Order. Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 267-271. doi: 10.4153/CMB-1978-047-1
@article{10_4153_CMB_1978_047_1,
     author = {Al-Abedeen, Ahmed Z. and Arora, H. L.},
     title = {A {Global} {Existence} and {Uniqueness} {Theorem} for {Ordinary} {Differential} {Equations} of {Generalized} {Order}},
     journal = {Canadian mathematical bulletin},
     pages = {267--271},
     year = {1978},
     volume = {21},
     number = {3},
     doi = {10.4153/CMB-1978-047-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-047-1/}
}
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