Browsing by Author "Hincal, Evren"

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Citation Count: Sabir, Zulqurnain;...et.al. (2022). "A hybrid computing approach to design the novel second order singular perturbed delay differential Lane-Emden model", Physica Scripta, Vol.97, No.8.
A hybrid computing approach to design the novel second order singular perturbed delay differential Lane-Emden model
(2022) Sabir, Zulqurnain; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Hincal, Evren; 56389
In this study, the mathematical form of the second order perturbed singular delay differential system is presented. The comprehensive features using the singular-point, perturbed factor and pantograph term are provided together with the shape factor of the second order perturbed singular delay differential system. The novel model is simulated numerically through the artificial neural networks (ANNs) based on the global/local optimization procedures, i.e., genetic algorithm (GA) and sequential quadratic programming (SQP). An activation function is constructed by using the differential model based on the second order perturbed singular delay differential system. The optimization of fitness function is performed through the hybrid computing strength of the ANNs-GA-SQP to solve the second order perturbed singular delay differential system. The exactness, substantiation, and authentication of the novel system is observed to solve three different variants of the novel model. The convergence, robustness, correctness, and stability of the numerical approach is performed using the comparison procedures of the available exact solutions. For the reliability, the statistical performances with necessary processes are provided using the ANNs-GA-SQP.
Citation Count: Tassaddiq, Asifa...et al. (2021). "A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior", Fractal and Fractional, Vol. 5, No. 4.
A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior
(2021) Tassaddiq, Asifa; Qureshi, Sania; Soomro, Amanullah; Hincal, Evren; Baleanu, Dumitru; Shaikh, Asif Ali; 56389
There is an increasing demand for numerical methods to obtain accurate approximate solutions for nonlinear models based upon polynomials and transcendental equations under both single and multivariate variables. Keeping in mind the high demand within the scientific literature, we attempt to devise a new nonlinear three-step method with tenth-order convergence while using six functional evaluations (three functions and three first-order derivatives) per iteration. The method has an efficiency index of about 1.4678, which is higher than most optimal methods. Convergence analysis for single and systems of nonlinear equations is also carried out. The same is verified with the approximated computational order of convergence in the absence of an exact solution. To observe the global fractal behavior of the proposed method, different types of complex functions are considered under basins of attraction. When compared with various well-known methods, it is observed that the proposed method achieves prespecified tolerance in the minimum number of iterations while assuming different initial guesses. Nonlinear models include those employed in science and engineering, including chemical, electrical, biochemical, geometrical, and meteorological models.
Citation Count: Sadri, Khadijeh...et.al. (2023). "A pseudo-operational collocation method for variable-order time-space fractional KdV-Burgers-Kuramoto equation", Mathematical Methods In The Applied Sciences, Vol.46, No.8, pp.8759-8778.
A pseudo-operational collocation method for variable-order time-space fractional KdV-Burgers-Kuramoto equation
(2023) Sadri, Khadijeh; Hosseini, Kamyar; Hincal, Evren; Baleanu, Dumitru; Salahshour, Soheil; 56389
The idea of this work is to provide a pseudo-operational collocation scheme to deal with the solution of the variable-order time-space fractional KdV-Burgers-Kuramoto equation (VOSTFKBKE). Such the fractional partial differential equation (FPDE) has three characteristics of dissipation, dispersion, and instability, which make this equation is used to model many phenomena in diverse fields of physics. Numerical solutions are sought in a linear combination of two-dimensional Jacobi polynomials as basis functions. In order to approximate unknown functions in terms of the basis vector, pseudo-operational matrices are constructed to avoid integration. An error bound of the residual function is estimated in a Jacobi-weighted space in the L2$$ {L}<^>2 $$ norms. Numerical results are compared with exact ones and those reported by other researchers to demonstrate the effectiveness of the recommended method.
Citation Count: Anbalagan, Pratap...et al. (2021). "A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks", AIMS Mathematics, Vol. 6, No. 5, pp. 4526-4555.
A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks
(2021) Anbalagan, Pratap; Hincal, Evren; Ramachandran, Raja; Baleanu, Dumitru; Cao, Jinde; Niezabitowski, Michal; 56389
This manuscript is concerned with the stability and synchronization for fractional-order delayed gene regulatory networks (FODGRNs) via Razumikhin approach. First of all, the existence of FODGRNs are established by using homeomorphism theory, 2-norm based on the algebraic method and Cauchy Schwartz inequality. The uniqueness of this work among the existing stability results are, the global Mittag-Letter stability of FODGRNs is explored based on the fractional-order Lyapunov Razumikhin approach. In the meanwhile, two different controllers such as linear feedback and adaptive feedback control, are designed respectively. With the assistance of fractional Razumikhin theorem and our designed controllers, we have established the global Mittag-Letter synchronization and adaptive synchronization for addressing master-slave systems. Finally, three numerical cases are given to justify the applicability of our stability and synchronization results.
Citation Count: Sadri, Khadijeh...et.al. (2023). "A robust scheme for Caputo variable-order time-fractional diffusion-type equations", Journal Of Thermal Analysis And Calorimetry, Vol.148, No.12, pp.5747-5764.
A robust scheme for Caputo variable-order time-fractional diffusion-type equations
(2023) Sadri, Khadijeh; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Sohei; Hincal, Evren; 56389
The focus of this work is to construct a pseudo-operational Jacobi collocation scheme for numerically solving the Caputo variable-order time-fractional diffusion-type equations with applications in applied sciences. Modeling scientific phenomena in the context of fluid flow problems, curing reactions of thermosetting systems, solid oxide fuel cells, and solvent diffusion into heavy oils led to the appearance of these equations. For this reason, the numerical solution of these equations has attracted a lot of attention. More precisely, using pseudo-operational matrices and appropriate approximations based on bivariate Jacobi polynomials, the approximate solutions of the variable-order time-fractional diffusion-type equations in the Caputo sense with high accuracy are formally retrieved. Based on orthogonal bivariate Jacobi polynomials and their operational matrices, a sparse algebraic system is generated which makes implementing the proposed approach easy. An error bound is computed for the residual function by proving some theorems. To illustrate the accuracy and efficiency of the scheme, several illustrative examples are considered. The results demonstrate the efficiency of the present method compared to those achieved by the Legendre and Lucas multi-wavelet methods and the Crank-Nicolson compact method.
Citation Count: Sabir, Zulqurnain...et.al. (2023). "Computational Performances Of Morlet Wavelet Neural Network For Solving A Nonlinear Dynamic Based On The Mathematical Model Of The Affection Of Layla And Majnun", Fractals, Vol.31, No.2.
Computational Performances Of Morlet Wavelet Neural Network For Solving A Nonlinear Dynamic Based On The Mathematical Model Of The Affection Of Layla And Majnun
(2023) Sabir, Zulqurnain; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Alshomrani, Ali S.; Hincal, Evren; 56389
The aim of this study is to design a novel stochastic solver through the Morlet wavelet neural networks (MWNNs) for solving the mathematical Layla and Majnun (LM) system. The numerical representations of the mathematical LM system have been presented by using the MWNNs along with the optimization is performed through the hybridization of the global and local search schemes. The local active-set (AS) and global genetic algorithm (GA) operators have been used to optimize an error-based merit function using the differential LM model and its initial conditions. The correctness of the MWNNs using the local and global operators is observed through the comparison of the obtained solutions and the Adams scheme, which is used as a reference solution. For the stability of the MWNNs using the global and local operators, the statistical performances with different operators have been provided using the multiple executions to solve the nonlinear LM system.
Citation Count: Yusuf, Abdullahi...et al. (2021). "Lump, its interaction phenomena and conservation laws to a nonlinear mathematical model", Journal of Ocean Engineering and Science.
Lump, its interaction phenomena and conservation laws to a nonlinear mathematical model
(2021) Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadir; Hincal, Evren; Baleanu, Dumitru; 56389
We solve the Ostrovsky equation in the absence of the rotation effect using the Hirota bilinear method and symbolic calculation. Some unique interaction phenomena have been obtained between lump solution, breather wave, periodic wave, kink soliton, and two-wave solutions. All the obtained solutions are validated by putting them into the original problem using the Wolfram Mathematica 12. The physical characteristics of the solutions have been visually represented to shed additional light on the acquired results. Furthermore, using the novel conservation theory, the conserved vectors of the governing equation have been generated. The discovered results are helpful in understanding particular physical phenomena in fluid dynamics as well as the dynamics of nonlinear higher dimensional wave fields in computational physics and ocean engineering and related disciplines. © 2021
Citation Count: Sabir, Zulqurnain;...et.al. (2023). "Meyer Wavelet Neural Networks Procedures To Investigate The Numerical Performances Of The Computer Virus Spread With Kill Signals", Fractals, Vol.31, No.2.
Meyer Wavelet Neural Networks Procedures To Investigate The Numerical Performances Of The Computer Virus Spread With Kill Signals
(2023) Sabir, Zulqurnain; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Alshomrani, Ali S.; Hincal, Evren; 56389
This study shows the design of the Meyer wavelet neural networks (WNNs) to perform the numerical solutions of the spread of computer virus with kill signals, i.e. SEIR-KS system. The optimization of the SEIR-KS system is performed by the Meyer WNNs together with the optimization through the genetic algorithm (GA) and sequential quadratic (SQ) programming, i.e. Meyer WNNs-GASQ programming. A sigmoidal-based log-sigmoid function is implemented as an activation function, while 10 numbers of neurons work with 120 variables throughout this study. The correctness of the proposed Meyer WNNs-GASQP programming is observed through the comparison of the obtained and reference numerical solutions. For the consistency and reliability of the Meyer WNNs-GASQ programming, an analysis based on different statistical procedures is performed using 40 numbers of independent executions. Moreover, the use of different statistical operators like mean, median, minimum, standard deviation and semi-interquartile range further validates the correctness of the Meyer WNNs-GASQ programming for solving the SEIR-KS system.
Citation Count: Korpinar, Zeliha...at all (2020). "Residual power series algorithm for fractional cancer tumor models", Alexandria Engineering Journal, Vol. 59, No. 3, pp. 1405-1412.
Residual power series algorithm for fractional cancer tumor models
(2020) Korpinar, Zeliha; Inc, Mustafa; Hincal, Evren; Baleanu, Dumitru; 56389
In this paper, the new series solutions of some fractional cancer tumor models are investigated by using residual power series method (RPSM). The RPSM is explained with Maclaurin expansion for the solution. One of the advantages of this method is quick and easy calculation to find series solutions by using mathematica software package. Graphical presentations for series solutions are given to explanation of the method. The obtained outcomes explain that process is applicable and reliable method to obtain numerical solutions of fractional equations. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation Count: Sulaiman, Tukur Abdulkadir...et al. (2022). "Two-wave, breather wave solutions and stability analysis to the (2+1)-dimensional Ito equation", JOURNAL OF OCEAN ENGINEERING AND SCIENCE, Vol. 7, No. 5, pp. 467-474.
Two-wave, breather wave solutions and stability analysis to the (2+1)-dimensional Ito equation
(2022) Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Hincal, Evren; Baleanu, Dumitru; Bayram, Mustafa; 56389
The current study employs the novel Hirota bilinear scheme to investigate the nonlinear model. Thus, we acquire some two-wave and breather wave solutions to the governing equation. Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process. Several recent investigations, on the other hand, imply that breathers can survive in more complex habitats, such as random seas, despite the attributed phys-ical restrictions. The authenticity and genuineness of all the acquired solutions agreed with the original equation. In order to shed more light on these novel solutions, we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values. The governing model is also stable because of the idea of linear stability. The study's findings may help explain the physics behind some of the chal-lenges facing ocean engineers.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )