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Interval Abel integral equation

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0 Published in 2017 at "Soft Computing"

DOI: 10.1007/s00500-015-1980-2

Abstract: In this paper, we use a generalization of the Riemann–Liouville fractional integral for interval-valued functions to study a theory of the interval Abel integral equation (IAIE). Our aim is to clarify under which suitable conditions… read more here.

Keywords: interval abel; integral equation; abel integral;

Abel’s integral operator: sparse representation based on multiwavelets

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0 Published in 2021 at "Bit Numerical Mathematics"

DOI: 10.1007/s10543-020-00832-1

Abstract: In this work, Abel’s integral operator is represented based on Alpert’s multiwavelets as a sparse matrix and then a non-linear Abel’s integral equation of the second kind is solved by multiwavelets Galerkin method. Nonlinearity and… read more here.

Keywords: representation based; integral operator; abel integral; operator sparse ... See more keywords

Solutions to Abel's Integral Equations in Distributions

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1 Published in 2018 at "Axioms"

DOI: 10.3390/axioms7030066

Abstract: The goal of this paper is to study fractional calculus of distributions, the generalized Abel’s integral equations, as well as fractional differential equations in the distributional space D ′ ( R + ) based on… read more here.

Keywords: equations distributions; integral equations; solutions abel; abel integral ... See more keywords

Uniqueness of Abel's Integral Equations of the Second Kind with Variable Coefficients

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1 Published in 2021 at "Symmetry"

DOI: 10.3390/sym13061064

Abstract: This paper studies the uniqueness of the solutions of several of Abel’s integral equations of the second kind with variable coefficients as well as an in-symmetry system in Banach spaces L(Ω) and L(Ω)×L(Ω), respectively. The… read more here.

Keywords: second kind; variable coefficients; kind variable; equations second ... See more keywords

Certain Solutions of Abel's Integral Equations on Distribution Spaces via Distributional Gα-Transform

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1 Published in 2022 at "Symmetry"

DOI: 10.3390/sym15010053

Abstract: Abel’s integral equation is an efficient singular integral equation that plays an important role in diverse fields of science. This paper aims to investigate Abel’s integral equation and its solution using Gα-transform, which is a… read more here.

Keywords: integral equation; abel integral; certain solutions; distribution ... See more keywords