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Hilfer-type fractional differential equations with variable coefficients

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  • Restrepo, Joel E.
  • Suragan, Durvudkhan

Abstract

In this paper, we give a representation of the solution of Hilfer-type fractional differential equations with continuous variable coefficients. The solution is represented by convergent infinite series involving composition of Riemann–Liouville fractional integral operators. The obtained representation of the solution can be used effectively for computational and analytic purposes. For the case of constant coefficients, the solution is given by the Riemann-Liouville fractional integral of the multivariate Mittag-Leffler function.

Suggested Citation

  • Restrepo, Joel E. & Suragan, Durvudkhan, 2021. "Hilfer-type fractional differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005002
    DOI: 10.1016/j.chaos.2021.111146
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    References listed on IDEAS

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    1. Baleanu, Dumitru & Restrepo, Joel E. & Suragan, Durvudkhan, 2021. "A class of time-fractional Dirac type operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Wang, JinRong & Zhang, Yuruo, 2015. "Nonlocal initial value problems for differential equations with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 850-859.
    3. Restrepo, Joel E. & Ruzhansky, Michael & Suragan, Durvudkhan, 2021. "Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions," Applied Mathematics and Computation, Elsevier, vol. 403(C).
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