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Well-posedness and numerical approximation of tempered fractional terminal value problems

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Abstract

For a class of tempered fractional terminal value problems of the Caputo type, we study the existence and uniqueness of the solution, analyze the continuous dependence on the given data, and using a shooting method we present and discuss three numerical schemes for the numerical approximation of such problems. Some numerical examples are considered in order to illustrate the theoretical results and evidence the efficiency of the numerical methods.

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Authors and Affiliations

  1. Centre of Mathematics, Pole CMAT-UTAD and Department of Mathematics, University of Trás-os-Montes e Alto Douro, UTAD Quinta de Prados 5001-801, Vila Real-, Portugal

    Maria Luísa Morgado

  2. Department of Mathematics and Centro de Matemática e Aplicações, Universidade NOVA de Lisboa Quinta da Torre, 2829-516, Caparica-, Portugal

    Magda Rebelo

Authors
  1. Maria Luísa Morgado
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  2. Magda Rebelo
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Correspondence to Maria Luísa Morgado.

Additional information

Dedicated to Professor Virginia Kiryakova on the occasion of her 65th birthday and the 20th anniversary of FCAA

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Morgado, M.L., Rebelo, M. Well-posedness and numerical approximation of tempered fractional terminal value problems. FCAA 20, 1239–1262 (2017). https://doi.org/10.1515/fca-2017-0065

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  • DOI: https://doi.org/10.1515/fca-2017-0065

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