Airy equation with memory involvement via Liouville differential operator

محورهای موضوعی : فصلنامه ریاضی

Bahram Agheli ¹ (Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran.)
Abdolali Neamaty ² (Department of Mathematics, University of Mazandaran, Babolsar, Iran.)
Mehdi Nategh ³ (Department of Mathematics, University of Mazandaran, Babolsar, Iran.)
Dumitru Baleanu ⁴ (Department of Mathematics, cankaya University, Ankara, Turkey.)

تاریخ دریافت : 1395/12/20 تاریخ پذیرش : 1396/08/13 تاریخ انتشار : 1396/01/12

کلید واژه: Fractional Calculus, Liuville differential operator, Airy function, Fractional Airy equation,

چکیده مقاله :

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.