Browsing by Author "İnç, Mustafa"

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A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana-Baleanu fractional derivatives
(Pergamon-Elsevier Science LTD, 2018) Baleanu, Dumitru; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
The model of transmission dynamics of vector-borne diseases with vertical transmission and cure within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced. The effect of vertical transmission and cure rate on the basic reproduction number is shown. The Atangana-Baleanu fractional operator in caputo sense (ABC) with non-singular and non-local kernels is used to study the model. The existence and uniqueness of solutions are investigated using the Picard-Lindel method. Ultimately, for illustrating the acquired results, we perform some numerical simulations and show graphically to observe the impact of the arbitrary order derivative. It is expected that the proposed model will show better approximation than the classical model established before. (C) 2018 Elsevier Ltd. All rights reserved.
A Homotopy Perturbation Solution for Solving Highly Nonlinear Fluid Flow Problem Arising in Mechanical Engineering
(Amer Inst Physics, 2018) Baleanu, Dumitru; Akgül, Ali; Faraz, Naeem; İnç, Mustafa; Akgül, Esra Karataş; Baleanu, Dumitru; 56389
In this paper, a highly nonlinear equations are treated analytically via homotopy perturbation method for fluid mechanics problem. The non-linear differential equations are transformed to a coupled non-linear ordinary, differential equations via similarity transformations. Graphical results are presented and discussed for various physical parameters.
A new approach for one-dimensional sine-Gordon equation
(Springer, 2016) Baleanu, Dumitru; İnç, Mustafa; Kılıçman, Adem; Baleanu, Dumitru; 56389
In this work, we use a reproducing kernel method for investigating the sine-Gordon equation with initial and boundary conditions. Numerical experiments are studied to show the efficiency of the technique. The acquired results are compared with the exact solutions and results obtained by different methods. These results indicate that the reproducing kernel method is very effective.
A New Fractional Hrsv Model and Its Optimal Control: A Non-Singular Operator Approach
(Elsevier B.V., 2020) Baleanu, Dumitru; Yusuf, Abdullahi; Baleanu, Dumitru; İnç, Mustafa; 56389
In the current work, a fractional version of SIRS model is extensively investigated for the HRSV disease involving a new derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The fixed-point theory is employed to show the existence and uniqueness of the solution for the model under consideration. In order to see the performance of this model, simulation and comparative analyses are carried out according to the real experimental data from the state of Florida. To believe upon the results obtained, the fractional order is allowed to vary between (0,1) whereupon the physical observations show that the fractional dynamical character depends on the order of derivative operator and approaches an integer solution as α tends to 1. These features make the model more applicable when presented in the structure of fractional-order with ABC derivative. The effect of treatment by an optimal control strategy is also examined on the evolution of susceptible, infectious, and recovered individuals. Simulation results indicate that our fractional modeling and optimal control scheme are less costly and more effective than the proposed approach in the classical version of the model to diminish the HRSV infected individuals.
A new method for approximate solutions of some nonlinear equations: Residual power series method
(Sage Publications LTD, 2016) Baleanu, Dumitru; Körpınar, Zeliha S.; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru
In this work, a powerful iterative method called residual power series method is introduced to obtain approximate solutions of nonlinear time-dependent generalized Fitzhugh-Nagumo equation with time-dependent coefficients and Sharma-Tasso-Olver equation subjected to certain initial conditions. The consequences show that this method is efficient and convenient, and can be applied to a large sort of problems. The approximate solutions are compared with the known exact solutions.
Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity
(Vinca Inst Nuclear Sci, 2019) Baleanu, Dumitru; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
In this paper, the residual power series method is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the residual power series method is efficient for examining numerical behavior of non-linear models. Further, the conservation of heat is studied using the multiplier method.
Approximate solutions to the conformable Rosenau-Hyman equation using the two-step Adomian decomposition method with Pade approximation
(Wiley, 2019) Baleanu, Dumitru; Aliyu, Aliyu Isa; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
This paper adopts the Adomian decomposition method and the Pade approximation techniques to derive the approximate solutions of a conformable Rosenau-Hyman equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing both the analytic and approximate solutions.
Beta derivative applied to dark and singular optical solitons for the resonance perturbed NLSE
(Springer Heidelberg, 2019) Baleanu, Dumitru; İnç, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; 56389
In this research we obtain some dark and singular solitons for the resonance perturbed nonlinear Schrodinger equation (NLSE) with beta derivative (BD). Two well-known analytical approaches have been utilised to extract the results. The constraints conditions are stated for the well-being and existence of the results. Some figures have been plotted to demonstrate the physical behavior of the obtained solutions.
Boundary value problem for nonlinear fractional differential equations of variable order via Kuratowski MNC technique
(2021) Baleanu, Dumitru; Baleanu, Dumitru; Souid, Mohammed Said; Hakem, Ali; İnç, Mustafa; 56389
In the present research study, for a given multiterm boundary value problem (BVP) involving the Riemann-Liouville fractional differential equation of variable order, the existence properties are analyzed. To achieve this aim, we firstly investigate some specifications of this kind of variable-order operators, and then we derive the required criteria to confirm the existence of solution and study the stability of the obtained solution in the sense of Ulam-Hyers-Rassias (UHR). All results in this study are established with the help of the Darbo's fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of our observed results.
Chirped Solitons in Negative Index Materials Generated By Kerr Nonlinearity
(Elsevier B.V., 2020) Baleanu, Dumitru; İnç, Mustafa; Doka, S. Y.; Akınlar, M. A.; Baleanu, Dumitru; 56389
In this paper, we are concerned with chirped solitary wave solutions in negative indexed materials having Kerr nonlinearity and self-phase modulation term. An auxiliary equation method together with an ansatz technique are employed. New chirped dark solitons, bright solitons, and trigonometric map solutions by using the auxiliary equation technique are obtained. Both 2- and 3-dimensional graphs are provided to illustrate the obtained results. The presented research will be useful especially for scientists who are studying solitons.
Combined Optical Solitary Waves and Conservation Laws For Nonlinear Chen-Lee-Liu Equation in Optical Fibers
(Elsevier GMBH, Urban & Fischer Verlag, 2018) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
This paper obtains a combined optical solitary wave solution that is modeled by nonlinear Chen-Lee-Liu equation (NCLE) which arises in the context of temporal pulses along optical fibers associated with the self-steepening nonlinearity using the complex envelope function ansatz. The novel combined solitary wave describes bright and dark solitary wave properties in the same expression. The intensity and the nonlinear phase shift of the combined solitary wave solution are reported. Moreover, the Lie point symmetry generators or vector fields of a system of partial differential equations (PDEs) which is acquired by transforming the NCLE to a real and imaginary parts are derived. It is observed that the obtained system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conservation laws (Cis) for the system using the general Cls theorem. Numerical simulation and physical interpretations of the obtained results are demonstrated with interesting figures showing the meaning of the acquired results. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the NCLE. (C) 2017 Elsevier GmbH. All rights reserved.
Combined optical solitary waves and conservation laws for. nonlinear Chen-Lee-Liu equation in optical fibers
(2018) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
This paper obtains a combined optical solitary wave solution that is modeled by nonlinear Chen-Lee-Liu equation (NCLE) which arises in the context of temporal pulses along optical fibers associated with the self-steepening nonlinearity using the complex envelope function ansatz. The novel combined solitary wave describes bright and dark solitary wave properties in the same expression. The intensity and the nonlinear phase shift of the combined solitary wave solution are reported. Moreover, the Lie point symmetry generators or vector fields of a system of partial differential equations (PDEs) which is acquired by transforming the NCLE to a real and imaginary parts are derived. It is observed that the obtained system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conservation laws (Cis) for the system using the general Cls theorem. Numerical simulation and physical interpretations of the obtained results are demonstrated with interesting figures showing the meaning of the acquired results. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the NCLE. (C) 2017 Elsevier GmbH. All rights reserved.
Comparison between the thermoelectric properties of new materials: The alloy of iron, vanadium, tungsten, and aluminum (Fe2V0.8W0.2Al) against an oxide such as NaCO2O4
(2021) Baleanu, Dumitru; Kaid, Noureddine; Ameur, Houari; İnç, Mustafa; Baleanu, Dumitru; Menni, Younes; Lorenzini, Giulio; 56389
An analysis of the thermoelectric characteristics of certain recently discovered materials is carried out in this investigation. The alloy of iron, vanadium, tungsten, and aluminum (Fe2V0.8W0.2Al) applied to a silicon crystal is compared to new inorganic thermoelectric materials, which are mosly oxides like NaCO2O4. For both materials, the thermoelectric effects, Seebeck effect, Peltier effect, Thomson effect, and Kelvin relations are described. The cooling rate's influence on the energy balance is also assessed. The traditional thermoelectric materials provided are mostly made up of toxic, rare and/or expensive elements, which makes large-scale thermoelectric generator integration difficult. In recent decades, research has shifted toward the development of novel materials with a better price-to-performance ratio. Despite a low conversion yield, the family of oxides offers significant benefits in this respect, which are particularly evident at high temperatures. The findings of our study indicated that Fe2V0.8W0.2 applied to a silicon crystal has good thermoelectric characteristics. A sufficient merit factor was found in the new substance under investigation.
Complexiton and Solitary Wave Solutions Of The Coupled Nonlinear Maccaris System Using Two Integration Schemes
(World Scientific Publ CO PTE LTD, 2018) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Nuray, Elif; 56389
In this paper, we consider a coupled nonlinear Maccaris system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.
Conservation laws, soliton-like and stability analysis for the time fractional dispersive long-wave equation
(Springer Open, 2018) Baleanu, Dumitru; İnç, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; 56389
In this manuscript we investigate the time fractional dispersive long wave equation (DLWE) and its corresponding integer order DLWE. The symmetry properties and reductions are derived. We construct the conservation laws (Cls) with Riemann-Liouville (RL) for the time fractional DLWE via a new conservation theorem. The conformable derivative is employed to establish soliton-like solutions for the governing equation by using the generalized projective method (GPM). Moreover, the Cls via the multiplier technique and the stability analysis via the concept of linear stability analysis for the integer order DLWE are established. Some graphical features are presented to explain the physical mechanism of the solutions.
Dark and Combined Optical Solitons, and Modulation Instability Analysis in Dispersive Metamaterial
(Elsevier GMBH, 2018) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
This paper obtains the dark and dark-bright or combined optical solitons to the nonlinear schrodinger equation (NLSE) describing propagation in dispersive metamaterial in optical fibers. The integration algorithm is the complex envelope function ansatz. This naturally lead to some constraint conditions placed on the soliton parameters which must hold for the solitons to exist. The intensities and the nonlinear phase shifts of the solitons are reported. Furthermore, the modulation instability analysis (MI) is studied based on the standard linear-stability analysis and the MI gain spectrum is got. Numerical simulation of some obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier GmbH. All rights reserved.
Dark and Singular Optical Solitons For The Conformable Space-Time Nonlinear Schrodinger Equation With Kerr and Power Law Nonlinearity
(Elsevier GMBH, Urban & Fischer Verlag, 2018) Baleanu, Dumitru; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; 56389
This paper extracts novel dark and singular optical solitons for the conformable space time nonlinear Schrodinger equation (CSTNLSE) with Kerr and power law nonlinearity by two integration schemes. The integration schemes are generalized tanh (GT), and Bernoulli (BL) sub-ODE methods. The constraints conditions for the existence of solitons are reported. The newly introduced fractional derivative called conformable derivative is used for extracting the soliton solutions. Numerical simulations of some of the obtained solutions are also presented. (C) 2018 Elsevier GmbH. All rights reserved.
Dark optical solitons and conservation laws to the resonance nonlinear Shrodinger's equation with Kerr law nonlinearity
(Elsevier GMBH, 2017) Baleanu, Dumitru; İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; 56389
In this work, we investigate the soliton solutions to the resonant nonlinear Shrodinger's equation (R-NSE) with Kerr law nonlinearity. By adopting the Riccati-Bernoulli sub-ODE technique, we present the exact dark optical, dark-singular and periodic singular soliton solutions to the model. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. We studied the R-NSE by analyzing a system of nonlinear partial differential equations (NPDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system, then we apply the general conservation theorem to establish a set of nontrivial and nonlocal conservation laws (Cls). Some interesting figures for the acquired solutions are Cls also presented.
Dark-bright optical solitary waves and modulation instability analysis with (2+1)-dimensional cubic-quintic nonlinear Schrodinger equation
(Taylor&Francis LTD, 2019) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
This paper addresses the (2+1)-dimensional cubic-quintic nonlinear Schrodinger equation (CQNLS) that serves as the model to study the light propagation through nonlinear optical media and non-Kerr crystals. A dark-bright optical solitary wave solution of this equation is retrieved by adopting the complex envelope function ansatz. This type of solitary wave describes the properties of bright and dark optical solitary waves in the same expression. The integration naturally lead to a constraint condition placed on the solitary wave parameters which must hold for the solitary waves to exist. Additionally, the modulation instability (MI) analysis of the model is studied based on the standard linear stability analysis and the MI gain spectrum is got. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CQNLS.
Dark-bright optical solitary waves and modulation instability analysis with (2+1)-dimensional cubic-quintic nonlinear Schrodinger equation
(2019) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullah; Baleanu, Dumitru; 56389
This paper addresses the (2+1)-dimensional cubic-quintic nonlinear Schrodinger equation (CQNLS) that serves as the model to study the light propagation through nonlinear optical media and non-Kerr crystals. A dark-bright optical solitary wave solution of this equation is retrieved by adopting the complex envelope function ansatz. This type of solitary wave describes the properties of bright and dark optical solitary waves in the same expression. The integration naturally lead to a constraint condition placed on the solitary wave parameters which must hold for the solitary waves to exist. Additionally, the modulation instability (MI) analysis of the model is studied based on the standard linear stability analysis and the MI gain spectrum is got. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CQNLS.