Browsing by Author "Isa Aliyu, Aliyu"

Now showing 1 - 5 of 5

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; Isa Aliyu, Aliyu
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: 3
Citation - Scopus: 3
Invariant Subspaces, Exact Solutions and Classification of Conservation Laws for a Coupled (1+1)-Dimensional Nonlinear Wu-Zhang Equation
(Iop Publishing Ltd, 2020) Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru; Aliyu, Aliyu Isa; Isa Aliyu, Aliyu
In this work, we apply the invariant subspace method to derive a set of invariant subspaces and solutions of the nonlinear Wu-Zhang equation which describes the dynamic behavior of dispersive long waves in fluid dynamics. The method gives logarithmic and polynomial solutions of the equation. Furthermore, the multipliers approach and new conservation theorem are employed to derive a set of conservation laws of the equation which are to the best of our knowledge reported for the first time in this work. The physical structure of the results is shown by figures of some special solutions in order to give us a better interpretation on the evolution of the solutions.
Citation - WoS: 10
Citation - Scopus: 14
Optical Solitons, Explicit Solutions and Modulation Instability Analysis With Second-Order Spatio-Temporal Dispersion
(Springer Heidelberg, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa; Isa Aliyu, Aliyu
This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the nonlinear Schrodinger equation (NLSE) with group velocity dispersion coefficient and second-order spatio-temporal dispersion coefficient, which arises in photonics and waveguide optics and in optical fibers. The integration algorithm is the sine-Gordon equation method (SGEM). Furthermore, the explicit solutions of the equation are derived by considering the power series solutions (PSS) theory and the convergence of the solutions is guaranteed. Lastly, the modulation instability analysis (MI) is studied based on the standard linear-stability analysis and the MI gain spectrum is obtained.
Citation - WoS: 23
Citation - Scopus: 28
Time Fractional Third-Order Variant Boussinesq System: Symmetry Analysis, Explicit Solutions, Conservation Laws and Numerical Approximations
(Springer Heidelberg, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Tchier, Fairouz; Isa Aliyu, Aliyu
The current work provides comprehensive investigation for the time fractional third-order variant Boussinesq system (TFTOBS) with Riemann-Liouville (RL) derivative. Firstly, we obtain point symmetries, similarity variables, similarity transformation and reduce the governing equation to a special system of ordinary differential equation (ODE) of fractional order. The reduced equation is in the Erdelyi-Kober (EK) sense. Secondly, we solve the reduced system of ODE using the power series (PS) expansion method. The convergence analysis for the power series solution is analyzed and investigated. Thirdly, the new conservation theorem and the generalization of the Noether operators are applied to construct nonlocal conservation laws (CLs) for the TFTOBS. Finally, we use residual power series (RPS) to extract numerical approximation for the governing equations. Interesting figures that explain the physical understanding for both the explicit and approximate solutions are also presented.
Citation - WoS: 104
Citation - Scopus: 107
Time-Fractional Cahn-Allen and Time-Fractional Klein-Gordon Equations: Lie Symmetry Analysis, Explicit Solutions and Convergence Analysis
(Elsevier Science Bv, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa; Isa Aliyu, Aliyu
This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented. (C) 2017 Elsevier B.V. All rights reserved.