Solutions to Abel’s Integral Equations in Distributions

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 inverse convolutional operators and Babenko's approach. Furthermore, we provide interesting applications of Abel's integral equations in viscoelastic systems, as well as solving other integral equations, such as π/2 θ y(ϕ) cos β ϕ(cos θ−cos ϕ) α dϕ = f (θ) , and ∞ 0 x 1/2 g(x)y(x + t)dx = f (t).

Solutions of the Generalized Abel’s Integral Equations of the Second Kind with Variable Coefficients

“…and convolution. Li et al [25][26][27] recently studied Abel's integral Equation (1) for any arbitrary α ∈ R in the generalized sense based on fractional calculus of distributions, inverse convolutional operators and Babenko's approach [28]. They obtained several new and interesting results that cannot be realized in the classical sense or by the Laplace transform.…”

Mathematical Analysis and Applications

“…Website: http://www.math.uvic.ca/faculty/harimsri/ This volume contains the invited, accepted and published submissions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]) to a Special Issue of the MDPI journal Axioms on the subject-area of "Mathematical Analysis and Applications".…”