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Subordination results for a class of multi-term fractional Jeffreys-type equations

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Abstract

Jeffreys equation and its fractional generalizations provide extensions of the classical diffusive laws of Fourier and Fick for heat and particle transport. In this work, a class of multi-term time-fractional generalizations of the classical Jeffreys equation is studied. Restrictions on the parameters are derived, which ensure that the fundamental solution to the one-dimensional Cauchy problem is a spatial probability density function evolving in time. The studied equations are recast as Volterra integral equations with kernels represented in terms of multinomial Mittag-Leffler functions. Applying operator-theoretic approach, we establish subordination results with respect to appropriate evolution equations of integer order, depending on the considered range of parameters. Analyticity of the corresponding solution operator is also discussed. The main tools in the proofs are Laplace transform and the Bernstein functions’ technique, especially, some properties of the sets of real powers of complete Bernstein functions.

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Acknowledgements

This work is supported by Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program and co-financed by the European Union through the European structural and Investment funds.

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  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, “Acad. G. Bontchev” Str., Block 8, 1113, Sofia, Bulgaria

    Emilia Bazhlekova

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Bazhlekova, E. Subordination results for a class of multi-term fractional Jeffreys-type equations. Fract Calc Appl Anal (2024). https://doi.org/10.1007/s13540-024-00275-3

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