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Öğe On the soliton solutions to the density-dependent space time fractional reaction-diffusion equation with conformable and M-truncated derivatives(Springer, 2023) Esen, Handenur; Ozdemir, Neslihan; Secer, Aydin; Bayram, Mustafa; Sulaiman, Tukur Abdulkadir; Ahmad, Hijaz; Yusuf, AbdullahiIn this manuscript, the density-dependent space-time fractional reaction-diffusion equation in the sense of conformable and M-truncated derivatives (CMD) is presented. Through fractional transformation, these nonlinear fractional equations can be converted into nonlinear ordinary differential equations (NLPDEs). Besides, with the help of the Riccati-Bernoulli sub-ODE method (RBM), new exact solutions for these nonlinear fractional equations are produced. In order to construct the comparative analysis between different type fractional derivatives, graphical representations are demonstrated for chosen values of unknown parameters.Öğe Optical solitons and other solutions to the Hirota-Maccari system with conformable, M-truncated and beta derivatives(World Scientific Publ Co Pte Ltd, 2022) Ozdemir, Neslihan; Esen, Handenur; Secer, Aydin; Bayram, Mustafa; Yusuf, Abdullahi; Sulaiman, Tukur AbdulkadirIn this research paper, we scrutinize the novel traveling wave solutions and other solutions with conformable, M-truncated and beta fractional derivatives for the nonlinear fractional Hirota-Maccari system. In order to acquire the analytical solutions, the Riccati-Bernoulli sub-ODE technique is implemented. Presented method is the very powerful technique to get the novel exact soliton and other solutions for nonlinear partial equations in sense of both integer and fractional-order derivatives. Mathematical properties of different kinds of fractional derivatives are given in this paper. A comparative approach is presented between the solutions with the fractional derivatives. For the validity of the solutions, the constraints conditions are determined. To illustrate the physical meaning of the presented equation, the 2D and 3D graphs of the acquired solutions are successfully charted by selecting appropriate values of parameters.Öğe Solitary wave solutions of chiral nonlinear Schrodinger equations(World Scientific Publ Co Pte Ltd, 2021) Esen, Handenur; Ozdemir, Neslihan; Secer, Aydin; Bayram, Mustafa; Sulaiman, Tukur Abdulkadir; Yusuf, AbdullahiThis paper presents the (1+1)-dimensional chiral nonlinear Schrodinger equation (1DCNLSE) and (2+1)-dimensional chiral nonlinear Schrodinger equation (2DCNLSE) that define the edge states of the fractional quantum hall effect. In this paper, we implement the Riccati-Bernoulli sub-ODE method in reporting the solutions of these two nonlinear physical models. As a result of this, some singular periodic waves, dark and singular optical soliton solutions are generated for these models. Some of the acquired solutions are illustrated by three-dimensional (3D) and two-dimensional (2D) graphs utilizing suitable values of the parameters with the help of the MAPLE software to demonstrate the importance in the real-world of the presented equations.