Browsing by Author "Aliyu, Aliyu Isa"

Now showing 1 - 20 of 80

Citation - WoS: 3
Citation - Scopus: 6
Adomian-Pade Approximate Solutions To the Conformable Non-Linear Heat Transfer Equation
(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
This paper adopts the Adomian decomposition method and the Pade approximation technique to derive the approximate solutions of a conformable heat transfer equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing the approximate solutions.
Citation - WoS: 1
An Analysis of Analytic and Approximate Solutions of the Nonlinear Foam-Drainage Equation and Its Applications
(Amer Scientific Publishers, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
In this study, the modified Kudryashov and Riccati-Bernoulli (sub-ODE) methods are applied to construct some analytical solutions of the nonlinear Foam-drainage equation which plays an important part in the formation and evolution of liquid foams. Kink type, singular and logarithmic function solutions are obtained. Then, the residual power series method (RPSM) is used to analyze the numerical behavior of the equation by considering all the exact solutions. We observed that the modified Kudryashov and Riccati Bernoulli sub-ODE methods are powerful techniques for finding the exact solutions to various nonlinear models. Also, the RPSM is efficient for examining numerical behavior of nonlinear models. Some interesting figures are shown to show the reliability of the methods.
Citation - WoS: 2
Citation - Scopus: 2
Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity
(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
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.
Citation - WoS: 12
Citation - Scopus: 16
Approximate Solutions To the Conformable Rosenau-Hyman Equation Using the Two-Step Adomian Decomposition Method With Pade Approximation
(Wiley, 2020) Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Akgul, Ali
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.
Citation - WoS: 15
Citation - Scopus: 16
Beta Derivative Applied To Dark and Singular Optical Solitons for the Resonance Perturbed Nlse
(Springer Heidelberg, 2019) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi
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.
Combined Optical Solitary Waves and Conservation Laws For Nonlinear Chen-Lee-Liu Equation in Optical Fibers
(Elsevier GMBH, Urban & Fischer Verlag, 2018) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru
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.
Citation - WoS: 38
Citation - Scopus: 39
Combined Optical Solitary Waves and Conservation Laws For. Nonlinear Chen-Lee Equation in Optical Fibers
(Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
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.
Citation - WoS: 32
Citation - Scopus: 35
Complexiton and Solitary Wave Solutions of the Coupled Nonlinear Maccaris System Using Two Integration Schemes
(World Scientific Publ Co Pte Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Nuray, Elif; Inc, Mustafa
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.
Citation - WoS: 24
Citation - Scopus: 26
Conservation Laws, Soliton-Like and Stability Analysis for the Time Fractional Dispersive Long-Wave Equation
(Springeropen, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi
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.
Citation - WoS: 15
Citation - Scopus: 17
Dark and Combined Optical Solitons, and Modulation Instability Analysis in Dispersive Metamaterial
(Elsevier Gmbh, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
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.
Citation - WoS: 40
Citation - Scopus: 41
Dark and Singular Optical Solitons for the Conformable Space-Time Nonlinear Schrodinger Equation With Kerr and Power Law Nonlinearity
(Elsevier Gmbh, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
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.
Citation - WoS: 40
Citation - Scopus: 35
Dark Optical Solitons and Conservation Laws To the Resonance Nonlinear Shrodinger's Equation With Kerr Law Nonlinearity
(Elsevier Gmbh, 2017) Yusuf, Abdullahi; Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru
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. (C) 2017 Elsevier GmbH. All rights reserved.
Dark-bright optical solitary waves and modulation instability analysis with (2+1)-dimensional cubic-quintic nonlinear Schrodinger equation
(Taylor&Francis LTD, 2019) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru
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.
Citation - WoS: 29
Citation - Scopus: 32
Dark-Bright Optical Solitary Waves and Modulation Instability Analysis With (2+1)-Dimensional Cubic-Quintic Nonlinear Schrodinger Equation
(Taylor & Francis Ltd, 2019) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
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.
Citation - WoS: 40
Citation - Scopus: 48
Dispersive Optical Solitons and Modulation Instability Analysis of Schrodinger-Hirota Equation With Spatio-Temporal Dispersion and Kerr Law Nonlinearity
(Academic Press Ltd- Elsevier Science Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the perturbed nonlinear Schrodinger-Hirota equation (SHE) with spatio-temporal dispersion (STD) and Kerr law nonlinearity in optical fibers. The integration algorithm is the Sine-Gordon equation method (SGEM). Furthermore, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis and the MI gain spectrum is got. (C) 2017 Elsevier Ltd. All rights reserved.
Dynamics of optical solitons, multipliers and conservation laws to the nonlinear schrodinger equation in (2+1)-dimensions with non-Kerr law nonlinearity
(2019) Aliyu, Aliyu Isa; Tchier, Fairouz; İnç, Mustafa; Yusuf, Abdullah; Baleanu, Dumitru
This work studies the (2 + 1)-dimensional nonlinear Schrodinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.
Citation - WoS: 25
Citation - Scopus: 24
Dynamics of Optical Solitons, Multipliers and Conservation Laws To the Nonlinear Schrodinger Equation in (2+1)-Dimensions With Non-Kerr Law Nonlinearity
(Taylor & Francis Ltd, 2019) Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa; Tchier, Fairouz; Inc, Mustafa
This work studies the (2 + 1)-dimensional nonlinear Schrodinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.
Citation - WoS: 35
Citation - Scopus: 38
Efficiency of the New Fractional Derivative With Nonsingular Mittag-Leffler Kernel To Some Nonlinear Partial Differential Equations
(Pergamon-elsevier Science Ltd, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi
In this work, the efficiency of the Atangana-Baleanu (AB) derivative over Caputo-Fabrizio (CF) to some nonlinear partial differential equation is presented. The considered equations are Rosenou-Haynam equation (RHE) and a class of mKdV (CmKdV) equation. The effective and efficient technique called the fractional homotopy perturbation transform method (FHPTM) is applied for the investigation of the governing equations. (C) 2018 Elsevier Ltd. All rights reserved.
Citation - WoS: 53
Citation - Scopus: 56
A Fractional Model of Vertical Transmission and Cure of Vector-Borne Diseases Pertaining To the Atangana-Baleanu Fractional Derivatives
(Pergamon-elsevier Science Ltd, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
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.
Citation - WoS: 17
Citation - Scopus: 19
Fractional Optical Solitons for the Conformable Space-Time Nonlinear Schrodinger Equation With Kerr Law Nonlinearity
(Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
In this work, we obtain new soliton solutions for the conformable space-time nonlinear Schrodinger equation (CSTNLSE) with Kerr law nonlinearity. Two integration schemes which are projective Ricatti and extended Jacobi elliptic function methods are applied to reach such solutions. The constraints conditions for the existence of soliton solutions are reported. Numerical simulations for some of the obtained solutions are presented.