One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-19,
author = {Ma\l gorzata Klimek},
title = {On contraction principle applied to nonlinear fractional differential equations with derivatives of order a [?] (0,1)},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {325-338},
zbl = {1273.34011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-19}
}
Małgorzata Klimek. On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1). Banach Center Publications, Tome 95 (2011) pp. 325-338. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-19/