Optical solitons of some fractional differential equations in nonlinear optics

This paper deals with two different forms of the conformable fractional Benjamin-Bona-Mahony (BBM) equations by an analytical method. These physical models have important applications for describing the propagation of optical pulses in non-linear media. The conformable fractional symmetric BBM equation and the conformable time fractional Equal-width (EW) equation are considered. The extended Jacobi's elliptic function expansion scheme are used to extract explicit solitons.