Differential Equations with Infinitely Many Derivatives and the Borel Transform

@article{Carlsson2016DifferentialEW,
  title={Differential Equations with Infinitely Many Derivatives and the Borel Transform},
  author={Marcus Carlsson and Humberto Prado and Enrique G. Reyes},
  journal={Annales Henri Poincar{\'e}},
  year={2016},
  volume={17},
  pages={2049-2074}
}
Differential equations with infinitely many derivatives, sometimes also referred to as “nonlocal” differential equations, appear frequently in branches of modern physics such as string theory, gravitation and cosmology. We properly interpret and solve linear equations in this class with a special focus on a solution method based on the Borel transform. This method is a far-reaching generalization of previous studies of nonlocal equations via Laplace and Fourier transforms, see for instance… CONTINUE READING