Browsing by Author "Kaplan M., Akbulut A."

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A Mathematical Analysis of a Model Involving an Integrable Equation for Wave Packet Envelope
(2022-01-01) Kaplan M., Akbulut A.; Kaplan, M, Akbulut, A
This study investigates new optical solutions to a model with an integrable equation for wave packet envelopes. For this purpose, we have employed two reliable techniques involving the modified extended tanh function and the exponential rational function procedures. We have also given the 3D graphics of the obtained solutions.
A novel exploration for traveling wave solutions to the integrable equation of wave packet envelope
(2022-06-01) Kaplan M., Akbulut A.
In this paper, with the aid of symbolic computation, different types of traveling wave solutions to a model involving an integrable equation for wave packet envelope have been presented. The exp(−Φ(ξ))-expansion and modified Kudryashov procedures have been adopted and finally 3D and 2D graphics of the obtained solutions have been plotted. The obtained results are including dark, breather, bright, and periodic soliton solutions.
Application of two different algorithms to the approximate long water wave equation with conformable fractional derivative
(2018-05-04) Kaplan M., Akbulut A.
The current paper devoted on two different methods to find the exact solutions with various forms including hyperbolic, trigonometric, rational and exponential functions of fractional differential equations systems with conformable farctional derivative. We have employed the modified simple equation and exp(Φ(ξ)) method here for the approximate long water wave equation. We have adopted here the fractional complex transform accompanied by properties of conformable fractional calculus for reduction of fractional partial differential equation systems to ordinary differential equation systems.
The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method
(2021-09-01) Kaplan M., Akbulut A.; Kaplan, M, Akbulut, A
In this study, we applied the generalized Kudryashov method to two different conformable fractional differential equations and one system namely Burgers’ equation with conformable derivative, Wu-Zhang system with conformable derivative, and the conformable sinh-Gordon equation. Obtained solutions are soliton-type solutions. All obtained solutions have been verified and considered correct by placing them in the original equation with the help of the Maple software program. Also, we have plotted three-dimensional (3D) graphs of some of these solutions with the help of Maple.