TY - JOUR
TI - Solution of Abel’s integral equation by Kashuri Fundo transform
AU - Cuha Fatma Aybike
AU - Peker Haldun Alpaslan
JN - Thermal Science
PY - 2022
VL - 26
IS - 4
SP - 3003
EP - 3010
PT - Article
AB - Integral equations can be defined as equations in which unknown function to  be determined appears under the integral sign. These equations have been  used in many problems occurring in different fields due to the connection  they establish with differential equations. Abel’s integral equation is an  important singular integral equation and Abel found this equation from a  problem of mechanics, namely the tautochrone problem. This equation and some  variants of it found applications in heat transfer between solids and gases  under non-linear boundary conditions, theory of superfluidity, subsolutions  of a non-linear diffusion problem, propagation of shock-waves in gas field  tubes, microscopy, seismology, radio astronomy, satellite photometry of  airglows, electron emission, atomic scattering, radar ranging, optical fiber  evaluation, X-ray radiography, flame and plasma diagnostics. Integral  transforms are widely used mathematical techniques for solving advanced  problems of applied sciences. One of these transforms is the Kashuri Fundo  transform. This transform was derived by Kashuri and Fundo to facilitate  the solution processes of ODE and PDE. In some works, it has been seen that  it provides great convenience in finding the unknown function in integral  equations. In this work, our aim is to solve Abel’s integral equation by  Kashuri Fundo transform and some applications are made to explain the  solution procedure of Abel’s integral equation by Kashuri Fundo transform.