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On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)

100%

Klimek M.

Banach Center Publications

2011

tom 95

nr 1

325-338

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.

Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order

63%

Klimek M., Błasik M.

Open Mathematics

2012

tom 10

nr 6

1981-1994

Two-term semi-linear and two-term nonlinear fractional differential equations (FDEs) with sequential Caputo derivatives are considered. A unique continuous solution is derived using the equivalent norms/metrics method and the Banach theorem on a fixed point. Both, the unique general solution connected to the stationary function of the highest order derivative and the unique particular solution generated by the initial value problem, are explicitly constructed and proven to exist in an arbitrary interval, provided the nonlinear terms fulfil the corresponding Lipschitz condition. The existence-uniqueness results are given for an arbitrary order of the FDE and an arbitrary partition of orders between the components of sequential derivatives.

Ograniczanie wyników

1 Banach Center Publications

1 Open Mathematics

2 Klimek M.

1 Błasik M.

1 2012

1 2011

Wyniki wyszukiwania

On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)

Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order