Abstract
We construct a fundamental solution for an ordinary differential equation with a distributed-order differentiation operator. The properties of the solution are studied. A Lagrange formula is obtained for distributed-order differential operators. A well-posed form of the Cauchy problem is found for the equation in question, and the solution of the problem is written using the Lagrange formula.
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ACKNOWLEDGMENTS
The author is keenly grateful to A.V. Pskhu for useful advice and comments, which were taken into consideration when writing this paper.
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Translated by V. Potapchouck
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Efendiev, B.I. Cauchy Problem for an Ordinary Differential Equation with a Distributed-Order Differentiation Operator. Diff Equat 56, 658–670 (2020). https://doi.org/10.1134/S0012266120050110
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DOI: https://doi.org/10.1134/S0012266120050110