Direct And Inverse Cauchy Problems For Generalized Space-Time Fractional Differential Equations

Joel E. Restrepo, Durvudkhan Suragan

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this paper, explicit solutions of a class of generalized space-time fractional Cauchy problems with time-variable coefficients are given. The representation of a solution involves kernels given by convergent infinite series of fractional integro-differential operators, which can be extensively and efficiently applied for analytic and computational goals. Time-fractional operators of complex orders with respect to a given function are used. Further, we study inverse Cauchy problems of finding time dependent coefficients for fractional wave and heat type equations, which involve the explicit representation of the solution of the direct Cauchy problem and a recent method to recover variable co-efficients for the considered inverse problems. Concrete examples and particular cases of the obtained results are discussed

Original languageEnglish
Pages (from-to)305-339
Number of pages35
JournalAdvances in Differential Equations
Volume26
Issue number7-8
Publication statusPublished - Jul 2021

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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