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Fractional relaxation of distributed order. (English) Zbl 1167.26303
Novak, Miroslav M., Complexus mundi. Emergent patterns in nature. Hackensack, NJ: World Scientific (ISBN 981-256-666-X/hbk). 33-42 (2006).

A detailed study of the distributed order fractional relaxation equation

0 1 b(β)u (β) (t)dβ=-λu(t)+q(t),t0,λ>0

subject to the initial condition u(0 + )=c 0 , where b(β)0, and 0 1 b(β)dβ=1 is carried out. In particular, the structure of its solution and in a few cases their asymptotic behaviour near zero and near infinity are also investigated.

26A33Fractional derivatives and integrals (real functions)
44A10Laplace transform
45J05Integro-ordinary differential equations