Airy equation with memory involvement via Liouville differential operator

International Journal of Mathematical Modelling & Computations

مقاله 2، دوره 7، 2 (SPRING) - شماره پیاپی 26، تیر 2017، صفحه 107-113   

نوع مقاله: Full Length Article

نویسندگان

Bahram Agheli^{* 1}؛ Abdolali Neamaty²؛ Mehdi Nategh²؛ Dumitru Baleanu³

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

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

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

چکیده

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.

کلیدواژه‌ها

Fractional Calculus؛ Liuville differential operator؛ Airy function؛ Fractional Airy equation