EXISTENCE FOR PARTIAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL CAUCHY-EULER OPERATOR

Lyubomir Boyadjiev, Pavel B. Dubovski, Jeffrey A. Slepoi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We investigate a boundary value problem for partial differential equation with Cauchy-Euler fractional operator x2αD∗,x2αu(x,y)+xαD∗,xαu(x,y)+uyy(x,y)=f(x,y),0<x<∞,0<y<1,0<α<1.The limitations on convergence of series and the Mellin transform lead to the search for solutions in the class of functions, which possess continuous fractional derivatives for x∈ (0 , 1) and equal to zero for x> 1. However, for some cases, the solution is found for the entire semi-infinite strip x> 0. The analysis is supported by the computations, which exhibit the high level of accuracy.

Original languageEnglish
Pages (from-to)285-294
Number of pages10
JournalJournal of Mathematical Sciences (United States)
Volume266
Issue number2
DOIs
StatePublished - Sep 2022

Keywords

  • Fractional Cauchy-Euler equation
  • Fractional partial differential equation
  • Mellin transform

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