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A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation

Journal Article


Abstract


  • The time-fractional diffusion-wave equation is revisited, where the time derivative is of order��2 �� and 0 < ����� 1. The behaviour of the equation is ���diffusion-like��� (respectively, ���wave-like���) when 0<�����12 (respectively, 12<�����1). Two types of time-fractional derivatives are considered, namely the Caputo and Riemann-Liouville derivatives. Initial value problems and initial-boundary value problems are studied and handled in a unified way using an embedding method. A two-parameter auxiliary function is introduced and its properties are investigated. The time-fractional diffusion equation is used to generate a new family of probability distributions, and that includes the normal distribution as a particular case.

Publication Date


  • 2022

Citation


  • Rodrigo, M. (2022). A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation. Fractional Calculus and Applied Analysis, 25(5), 1757-1784. doi:10.1007/s13540-022-00087-3

Scopus Eid


  • 2-s2.0-85138374118

Web Of Science Accession Number


Start Page


  • 1757

End Page


  • 1784

Volume


  • 25

Issue


  • 5

Place Of Publication


Abstract


  • The time-fractional diffusion-wave equation is revisited, where the time derivative is of order��2 �� and 0 < ����� 1. The behaviour of the equation is ���diffusion-like��� (respectively, ���wave-like���) when 0<�����12 (respectively, 12<�����1). Two types of time-fractional derivatives are considered, namely the Caputo and Riemann-Liouville derivatives. Initial value problems and initial-boundary value problems are studied and handled in a unified way using an embedding method. A two-parameter auxiliary function is introduced and its properties are investigated. The time-fractional diffusion equation is used to generate a new family of probability distributions, and that includes the normal distribution as a particular case.

Publication Date


  • 2022

Citation


  • Rodrigo, M. (2022). A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation. Fractional Calculus and Applied Analysis, 25(5), 1757-1784. doi:10.1007/s13540-022-00087-3

Scopus Eid


  • 2-s2.0-85138374118

Web Of Science Accession Number


Start Page


  • 1757

End Page


  • 1784

Volume


  • 25

Issue


  • 5

Place Of Publication