title: Periodicity and positivity of a class of fractional differential equations.
abstract: Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.
authors.affiliation: Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia.
authors.forename: Rabha W
authors.initials: RW
authors.lastname: Ibrahim
authors.affiliation: Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Perlis Malaysia.
authors.forename: M Z
authors.initials: MZ
authors.lastname: Ahmad
authors.affiliation: Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Perlis Malaysia.
authors.forename: M Jasim
authors.initials: MJ
authors.lastname: Mohammed
keywords: Fractional calculus; Fractional differential equations; Rayleigh equation