Airy equation with memory involvement via Liouville differential operator

Document Type: Full Length Article


1 Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran.

2 Department of Mathematics, University of Mazandaran, Babolsar, Iran.

3 Department of Mathematics, cankaya University, Ankara, Turkey.


In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form.
A similar suggestion to the right FADE, converts it into an equation in the Laplace domain.
An illustration to the approximation and asymptotic behavior of the integral solution to the left FADE with respect to the existing parameters is presented.