Solution of Abel’s integral equation by Kashuri Fundo transform

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.