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On linear fractional differential equations with variable coefficients

Author

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  • Fernandez, Arran
  • Restrepo, Joel E.
  • Suragan, Durvudkhan

Abstract

We study and solve linear ordinary differential equations, with fractional order derivatives of either Riemann–Liouville or Caputo types, and with variable coefficients which are either integrable or continuous functions. In each case, the solution is given explicitly by a convergent infinite series involving compositions of fractional integrals, and its uniqueness is proved in suitable function spaces using the Banach fixed point theorem. As a special case, we consider the case of constant coefficients, whose solutions can be expressed by using the multivariate Mittag–Leffler function. Some illustrative examples with potential applications are provided.

Suggested Citation

  • Fernandez, Arran & Restrepo, Joel E. & Suragan, Durvudkhan, 2022. "On linear fractional differential equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    • Handle: RePEc:eee:apmaco:v:432:y:2022:i:c:s0096300322004441
    DOI: 10.1016/j.amc.2022.127370
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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. 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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    Cited by:

    1. Lu, Xin & Chen, Ning & Li, Hui & Guo, Shiyu & Chen, Zengtao, 2023. "Simulation of the temperature distribution of lithium-ion battery module considering the time-delay effect of the porous electrodes," Energy, Elsevier, vol. 284(C).
    2. Irgashev, B.Yu., 2023. "Initial boundary value problem for a high-order equation with two lines of degeneracy with the Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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