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Inverse problem for a multi-parameters space-time fractional diffusion equation with nonlocal boundary conditions: operational calculus approach

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Abstract

An inverse problem for determining a time dependent source term and diffusion concentration for a diffusion equation involving \(n+1\) Caputo fractional derivatives of different orders in time (multi-parameters) is considered. The spectral problem involves the composition of Caputo and Riemann–Liouville fractional derivatives. The existence of unique solution of the inverse problem is proved by using different estimates of multinomial Mittag-Leffler function.

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Author notes

  1. Sara Aziz and Salman A. Malik have contributed equally to this work.

Authors and Affiliations

  1. Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad, Pakistan

    Muhammad Ali & Sara Aziz

  2. Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

    Salman A. Malik

Authors
  1. Muhammad Ali
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  2. Sara Aziz
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  3. Salman A. Malik
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Ali, M., Aziz, S. & Malik, S.A. Inverse problem for a multi-parameters space-time fractional diffusion equation with nonlocal boundary conditions: operational calculus approach. J. Pseudo-Differ. Oper. Appl. 13, 3 (2022). https://doi.org/10.1007/s11868-021-00434-7

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  • DOI: https://doi.org/10.1007/s11868-021-00434-7

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