scholarly journals Analytical solution of Abel integral equation arising in astrophysics via Laplace transform

2015 ◽  
Vol 23 (1) ◽  
pp. 102-107 ◽  
Author(s):  
Sunil Kumar ◽  
Amit Kumar ◽  
Devendra Kumar ◽  
Jagdev Singh ◽  
Arvind Singh
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Laplace Transform ◽  
Abel Integral Equation

scholarly journals About Solution of the Nonlinear Generalized Abel Integral Equation

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Burkhan Kalimbetov
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Power Function ◽  
Nuclear Physics ◽  
Abel Equation ◽  
Abel Integral Equation ◽  
Spatial Graphs

As is known, many problems of electronics, nuclear physics, optics and astrophysics, etc. are described by the Abel integral equation of the first kind. In this paper we consider the nonlinear generalized Abel equation and show that its solution can be represented as an integral of a power function. It is shown that the constructed analytical solution and the symbolic solution obtained by means of the computer mathematics system Maple coincides, and their planar and spatial graphs are presented.

scholarly journals On the numerical solution of an Abel integral equation

1979 ◽  
Vol 16 (3) ◽  
pp. 497-503
Author(s):  
R. Smarzewski ◽  
H. Malinowski
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Abel Integral Equation

scholarly journals Analytical solution to local fractional Landau-Ginzburg-Higgs equation on fractal media

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4449-4455
Author(s):  
Shu-Xian Deng ◽  
Xin-Xin Ge
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Present Article ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Fractal Media

The main objective of the present article is to introduce a new analytical solution of the local fractional Landau-Ginzburg-Higgs equation on fractal media by means of the local fractional variational iteration transform method, which is coupling of the variational iteration method and Yang-Laplace transform method.

Anomalous diffusion equation using a new general fractional derivative within the Miller–Ross kernel

2020 ◽  
Vol 34 (27) ◽  
pp. 2050289
Author(s):  
Yiying Feng ◽  
Jiangen Liu
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Anomalous Diffusion ◽  
Fractional Integral ◽  
Liouville Type

In view of the generalization of Miller–Ross kernel in the sense of Riemann–Liouville type, we propose the new definitions of the general fractional integral (GFI) and general fractional derivative (GFD) to discuss the anomalous diffusion equation, which is distinct from those classic calculus operators. The obtained analytical solution of the application described in the graph is effective and accurate making the use of Laplace transform.

Analytical solutions of citrate–phosphate coupled model of rice (Oryza sativa L.) roots

2020 ◽  
Vol 13 (07) ◽  
pp. 2050061
Author(s):  
Huiping Zhang ◽  
Shuyue Wang ◽  
Zhonghui Ou
Keyword(s):  
Oryza Sativa ◽  
Analytical Solution ◽  
Laplace Transform ◽  
Oryza Sativa L ◽  
Coupled Model ◽  
Inverse Laplace Transform ◽  
Citrate Solution ◽  
Separation Variable ◽  
The Laplace Transform ◽  
Citrate Phosphate

The citrate secreted by the rice (Oryza sativa L.) roots will promote the absorption of phosphate, and this process is described by the Kirk model. In our work, the Kirk model is divided into citrate sub-model and phosphate sub-model. In the citrate sub-model, we obtain the analytical solution of citrate with the Laplace transform, inverse Laplace transform and convolution theorem. The citrate solution is substituted into the phosphate sub-model, and the analytical solution of phosphate is obtained by the separation variable method. The existence of the solutions can be proved by the comparison test, the Weierstrass M-test and the Abel discriminating method.

scholarly journals Newtonsche Aufheizung, Abelsche Integralgleichungen zweiter Art und Mittag-Leffler-Funktionen

1987 ◽  
Vol 42 (10) ◽  
pp. 1141-1146 ◽  
Author(s):  
Rudolf Gorenflo
Keyword(s):  
Integral Equation ◽  
Explicit Solution ◽  
Temporal Evolution ◽  
Plane Boundary ◽  
Qualitative Properties ◽  
Boundary Temperature ◽  
Abel Integral Equation ◽  
Homogeneous Half Space ◽  
Interior Boundary ◽  
The Difference

The problem of heating a homogeneous half-space by radiation from outside across the plane boundary is considered. Newtonian heating means that the heat flux across the boundary is proportional to the difference of outside temperature and interior boundary temperature. The outside temperature is assumed to be constant and positive, the initial inside temperature is zero everywhere. The problem is onedim ensional in space. The temporal evolution of the inward boundary temperature obeys an Abel integral equation of second kind for whose explicit solution three methods are described (one by Laplace transform , the other two by infinite series defining the Mittag-Leffler function of index 1/2). The explicit solution facilitates discussion of its qualitative properties. Finally, the general Abel integral equation of second kind is treated by Mittag-Leffler functions.

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