Browsing by Author "Kaplan, M."

Now showing 1 - 9 of 9

A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces
(2024.01.01) Okeke, G.A.; Ugwuogor, C.I.; Alqahtani, R.T.; Kaplan, M.; Ahmed, W.E.
We introduce the modified Picard-Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized phi-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard-Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature.
A novel iterative scheme for solving delay differential equations and third order boundary value problems via Green's functions
(2024.01.01) Okeke, G.A.; Udo, A.V.; Alqahtani, R.T.; Kaplan, M.; Ahmed, W.E.
In this paper, we constructed a novel fixed point iterative scheme called the Modified-JK iterative scheme. This iteration process is a modification of the JK iterative scheme. Our scheme converged weakly to the fixed point of a nonexpansive mapping and strongly to the fixed point of a mapping satisfying condition (E). We provided some examples to show that the new scheme converges faster than some existing iterations. Stability and data dependence results were proved for this iteration process. To substantiate our results, we applied our results to solving delay differential equations. Furthermore, the newly introduced scheme was applied in approximating the solution of a class of third order boundary value problems (BVPs) by embedding Green's functions. Moreover, some numerical examples were presented to support the application of our results to BVPs via Green's function. Our results extended and generalized other existing results in literature.
A novel iterative scheme for solving delay differential equations and third order boundary value problems via Green’s functions
(American Institute of Mathematical Sciences, 2024) Okeke, G.A.; Udo, A.V.; Alqahtani, R.T.; Kaplan, M.; Ahmed, W.E.
In this paper, we constructed a novel fixed point iterative scheme called the Modified-JK iterative scheme. This iteration process is a modification of the JK iterative scheme. Our scheme converged weakly to the fixed point of a nonexpansive mapping and strongly to the fixed point of a mapping satisfying condition (E). We provided some examples to show that the new scheme converges faster than some existing iterations. Stability and data dependence results were proved for this iteration process. To substantiate our results, we applied our results to solving delay differential equations. Furthermore, the newly introduced scheme was applied in approximating the solution of a class of third order boundary value problems (BVPs) by embedding Green’s functions. Moreover, some numerical examples were presented to support the application of our results to BVPs via Green’s function. Our results extended and generalized other existing results in literature.
A unique computational investigation of the exact traveling wave solutions for the fractional-order Kaup-Boussinesq and generalized Hirota Satsuma coupled KdV systems arising from water waves and interaction of long waves
(2024.01.01) Wang, X.F.; Yue, X.G.; Kaabar, M.K.A.; Akbulut, A.; Kaplan, M.
A novel technique, named auxiliary equation method, is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems: the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional derivative. Our solutions were obtained using MAPLE software. This technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean engineering. Since a standard equation has not been used as an auxiliary equation for this technique, different and novel solutions are obtained via this technique.
Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation
(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Alqahtani, R.T.; Kaplan, M.
This work focuses on the utilization of the generalized exponential rational function method (GERFM) to analyze wave propagation of the extended (3 + 1)-dimensional Sakovich equation. The demonstrated effectiveness and robustness of the employed method underscore its relevance to a wider spectrum of nonlinear partial differential equations (NPDEs) in physical phenomena. An examination of the physical characteristics of the generated solutions has been conducted through two- and three-dimensional graphical representations.
Analyzing Soliton Solutions of the Extended (3+1)-Dimensional Sakovich Equation
(2024.01.01) Alqahtani, RT.; Kaplan, M.
This work focuses on the utilization of the generalized exponential rational function method (GERFM) to analyze wave propagation of the extended (3 + 1)-dimensional Sakovich equation. The demonstrated effectiveness and robustness of the employed method underscore its relevance to a wider spectrum of nonlinear partial differential equations (NPDEs) in physical phenomena. An examination of the physical characteristics of the generated solutions has been conducted through two- and three-dimensional graphical representations.
Multiple soliton and traveling wave solutions of the negative-order-KdV-CBS model
(2024.01.01) Raza, N.; Arshed, S.; Kaplan, M.
The (3+1) -dimensional new negative-order-KdV-CBS model is investigated in this study. The suggested model combines the Korteweg-de Vries (KdV) and Calogero-Bogoyavlenskii-Schiff (CBS) equations. This research provides multiple soliton solutions and traveling wave solutions for the KdV-CBS model. Multiple exp-function methods have been used for extracting soliton solutions. For this aim, the extended sinh-Gordon equation expansion approach was selected to get traveling wave solutions. The findings are graphically examined by selecting appropriate values for arbitrary parameters.
On the Dynamics of the Complex Hirota-Dynamical Model
(2023) Akbulut, A.; Kaplan, M.; Alqahtani, R.T.; Ahmed, W.E.
The complex Hirota-dynamical Model (HDM) finds multifarious applications in fields such as plasma physics, fusion energy exploration, astrophysical investigations, and space studies. This study utilizes several soliton-type solutions to HDM via the modified simple equation and generalized and modified Kudryashov approaches. Modulation instability (MI) analysis is investigated. We also offer visual representations for the HDM.
Wave Propagation and Stability Analysis for Ostrovsky and Symmetric Regularized Long-Wave Equations
(2023.01.01) Kaplan, M.; Alqahtani, R.T.; Alharthi, N.H.
This work focuses on the propagation of waves on the water's surface, which can be described via different mathematical models. Here, we apply the generalized exponential rational function method (GERFM) to several nonlinear models of surface wave propagation to identify their multiple solitary wave structures. We provide stability analysis and graphical representations for the considered models. Additionally, this paper compares the results obtained in this work and existing solutions for the considered models in the literature. The effectiveness and potency of the utilized approach are demonstrated, indicating their applicability to a broad range of nonlinear partial differential equations in physical phenomena.