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Distributed order equations as boundary value problems. (English) Zbl 1268.45005
Summary: There has been a recent increase in interest in the use of distributed order differential equations (particularly in the case where the derivatives are given in the Caputo sense) to model various phenomena. Recent papers have provided insights into the numerical approximation of the solution, and some results on existence and uniqueness have been proved. In each case, the representation of the solution depends, among other parameters, on Caputo-type initial conditions. In this paper we discuss the existence and uniqueness of solutions and we propose a numerical method for their approximation in the case where the initial conditions are not known and, instead, some Caputo-type conditions are given away from the origin.

MSC:
45J05 Integro-ordinary differential equations
65R20 Numerical methods for integral equations
34A08 Fractional ordinary differential equations and fractional differential inclusions
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