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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.
Małgorzata Klimek. "On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)." Banach Center Publications 95.1 (2011): 325-338. <http://eudml.org/doc/282401>.
@article{MałgorzataKlimek2011, abstract = {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.}, author = {Małgorzata Klimek}, journal = {Banach Center Publications}, keywords = {fractional differential equation; fractional derivative; fixed point theorem; equivalent norms}, language = {eng}, number = {1}, pages = {325-338}, title = {On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)}, url = {http://eudml.org/doc/282401}, volume = {95}, year = {2011}, }
TY - JOUR AU - Małgorzata Klimek TI - On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1) JO - Banach Center Publications PY - 2011 VL - 95 IS - 1 SP - 325 EP - 338 AB - 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. LA - eng KW - fractional differential equation; fractional derivative; fixed point theorem; equivalent norms UR - http://eudml.org/doc/282401 ER -