Solutions of a class of n-th order ordinary and partial differential equations via fractional calculus

Shih Tong Tu, Wen Chieh Luo, Erh-Tsung Chin

Research output: Contribution to journalArticle

Abstract

Solutions of the n-th order linear ordinary differential equations (z + b)lΠn-1k=1(z+ak)φn + ∑nk=1φn-k{Cλk{Q(z)}k + Cλk-1{G(z)}k-1} = f (z ≠ -ak (k = 1,2,...,n - 1) z ≠-b; ai ≠ aj ≠ b i f i ≠ j; n > l, l ≥ 2) and the partial differential equations (z + b)lΠn-1k=1(z + ak) · ∂nμ/∂zn + ∑n-1k=1n-kμ/∂zn-k{Cλ k{Q(z)}k + Cλk-1{G(z)}k-1} +αμ(z,t) = M∂2μ/∂t2 + N∂μ/∂t (z ≠ -ak (k= 1,2,...,n-l) z ≠ -b; ai ≠ aj ≠ b i f i ≠ j; n > l, l ≥ 2) are discussed.

Original languageEnglish
Pages (from-to)499-515
Number of pages17
JournalTaiwanese Journal of Mathematics
Volume1
Issue number4
DOIs
Publication statusPublished - 1997 Jan 1

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Linear Ordinary Differential Equations
Fractional Calculus
Ordinary differential equation
Partial differential equation
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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title = "Solutions of a class of n-th order ordinary and partial differential equations via fractional calculus",
abstract = "Solutions of the n-th order linear ordinary differential equations (z + b)lΠn-1k=1(z+ak)φn + ∑nk=1φn-k{Cλk{Q(z)}k + Cλk-1{G(z)}k-1} = f (z ≠ -ak (k = 1,2,...,n - 1) z ≠-b; ai ≠ aj ≠ b i f i ≠ j; n > l, l ≥ 2) and the partial differential equations (z + b)lΠn-1k=1(z + ak) · ∂nμ/∂zn + ∑n-1k=1 ∂n-kμ/∂zn-k{Cλ k{Q(z)}k + Cλk-1{G(z)}k-1} +αμ(z,t) = M∂2μ/∂t2 + N∂μ/∂t (z ≠ -ak (k= 1,2,...,n-l) z ≠ -b; ai ≠ aj ≠ b i f i ≠ j; n > l, l ≥ 2) are discussed.",
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Solutions of a class of n-th order ordinary and partial differential equations via fractional calculus. / Tu, Shih Tong; Luo, Wen Chieh; Chin, Erh-Tsung.

In: Taiwanese Journal of Mathematics, Vol. 1, No. 4, 01.01.1997, p. 499-515.

Research output: Contribution to journalArticle

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