Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order

Abstract EN

This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus.

The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type.

The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.