Borel summability for fractional differential equation in the unit disk

Rabha W. Ibrahim, Maslina Darus

Research output: Contribution to journalArticle

Abstract

In this article, we consider some classes of nonlinear fractional differential equations with singularity take the form tααu(t,z)/∂tα=F(t,z,u,∂u/∂z) 0<α<1, where t ∈ J:= [0,1] and z ∈ U:= {z ∈ C: z < 1}. Our purpose is to establish a result similar to the k-summability known in the case of singular ordinary differential equations. It's shown that, under some conditions, all formal solutions are Borel summable or k-summable with respect to z ∈ U in all directions except at most a countable number.

Original languageEnglish
Pages (from-to)339-344
Number of pages6
JournalProceedings of the Pakistan Academy of Sciences
Volume50
Issue number4
Publication statusPublished - Dec 2013
Externally publishedYes

Keywords

  • Borel summable
  • Fractional calculus
  • Fractional differential equation
  • Holomorphic solution
  • Nonlinear
  • Riemann-liouville operators
  • Singular fractional differential equation
  • Unit disk

ASJC Scopus subject areas

  • Social Sciences(all)

Cite this

Borel summability for fractional differential equation in the unit disk. / Ibrahim, Rabha W.; Darus, Maslina.

In: Proceedings of the Pakistan Academy of Sciences, Vol. 50, No. 4, 12.2013, p. 339-344.

Research output: Contribution to journalArticle

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