On Generalized Solutions of Locally Fuchsian Ordinary Differential Equations

Mirumbe, G. I.; Mango, John Magero

doi:10.18642/jmsaa_7100121959

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2023

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This can be easily checked by using Formula (17). Furthermore, the distributional solutions of some classes of Cauchy-Euler equations have been studied by many researchers; see [2][3][4][5][6][7][8][9] for more details.…”

Section: Introductionmentioning

confidence: 99%

Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind

et al. 2023

View full text Add to dashboard Cite

In this work, we employed the Laplace transform of right-sided distributions in conjunction with the power series method to obtain distributional solutions to the modified Bessel equation and its related equation, whose coefficients contain the parameters ν and γ. We demonstrated that the solutions can be expressed as finite linear combinations of the Dirac delta function and its derivatives, with the specific form depending on the values of ν and γ.

show abstract

Section: Introductionmentioning

confidence: 99%

Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind

et al. 2023

View full text Add to dashboard Cite

show abstract

“…The distributional solutions with higher order of Cauchy-Euler equations were studied by many researchers; see [2][3][4][5][6][7][8] for more details.…”

Section: Introductionmentioning

confidence: 99%

Finite Series of Distributional Solutions for Certain Linear Differential Equations

Waiyaworn

Nonlaopon

Orankitjaroen

2020

Axioms

View full text Add to dashboard Cite

In this paper, we present the distributional solutions of the modified spherical Bessel differential equations t2y′′(t)+2ty′(t)−[t2+ν(ν+1)]y(t)=0 and the linear differential equations of the forms t2y′′(t)+3ty′(t)−(t2+ν2−1)y(t)=0, where ν∈N∪{0} and t∈R. We find that the distributional solutions, in the form of a finite series of the Dirac delta function and its derivatives, depend on the values of ν. The results of several examples are also presented.

show abstract

On Generalized Solutions of Locally Fuchsian Ordinary Differential Equations

Abstract: We consider an m-th order constant coefficient locally Fuchsian ordinary differential equation at the origin

Cited by 2 publications

References 6 publications

Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind

Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind

Finite Series of Distributional Solutions for Certain Linear Differential Equations

Contact Info

Product

Resources

About