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Initial value/boundary value problem for composite fractional relaxation equation

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  • Mophou, G.
  • Tao, S.
  • Joseph, C.

Abstract

We consider initial value/boundary value problem for composite fractional relaxation equation involving Caputo fractional derivative of order 0<β<1. We prove by means of change of variable that this problem is reduced to initial value/boundary value problem for fractional diffusion equation involving Riemann–Liouville fractional derivative of order β=1-α. Then by means of eigenfunctions expansions, we establish the existence and uniqueness of solution.

Suggested Citation

  • Mophou, G. & Tao, S. & Joseph, C., 2015. "Initial value/boundary value problem for composite fractional relaxation equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 134-144.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:134-144
    DOI: 10.1016/j.amc.2014.09.081
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    References listed on IDEAS

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    1. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
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    1. Addai, Isaac & Asiedu, Henry Kwasi & Barnes, Benedict, 2025. "The exact solution of the composite fractional differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    2. Gisèle Mophou, 2017. "Optimal Control for Fractional Diffusion Equations with Incomplete Data," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 176-196, July.
    3. Bahaa, G.M., 2019. "Optimal control problem for variable-order fractional differential systems with time delay involving Atangana–Baleanu derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 129-142.

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