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Papers by maasoomah sadaf

Research paper thumbnail of Construction of new solutions of Korteweg-de Vries Caudrey-Dodd-Gibbon equation using two efficient integration methods

PLOS ONE, 2022

Korteweg-de Vries Caudrey-Dodd-Gibbon (KdV-CDG) equation describes many physical phenomena in pla... more Korteweg-de Vries Caudrey-Dodd-Gibbon (KdV-CDG) equation describes many physical phenomena in plasma physics, optical fibers, dynamics of the ocean, quantum mechanics, acoustic waves and laser optical applications. In this paper, the KdV-CDG equation is analyzed via two reliable and efficient integrating approaches. The suggested techniques; the extended G 0 G 2-expansion method and exponential (ψ(ξ))-expansion method successfully extract hyperbolic function solutions, trigonometric function solutions and rational function solutions. The existence criteria for all the obtained solutions are also discussed in this paper. At the end, various 3D and 2D contour plots have been constructed for better understanding of constructed solutions.

Research paper thumbnail of Extraction of new exact solutions of the resonant fractional nonlinear Schrödinger equation via two integrating techniques

Optical and Quantum Electronics

Research paper thumbnail of Dynamics investigation of the (4+1)-dimensional Fokas equation using two effective techniques

Research paper thumbnail of Optical soliton solutions of fractional Sasa-Satsuma equation with beta and conformable derivatives

Optical and Quantum Electronics

Research paper thumbnail of Optical solitons for the complex Ginzburg–Landau equation with Kerr law and non-Kerr law nonlinearity

Optical and Quantum Electronics

Research paper thumbnail of Exact soliton and solitary wave solutions to the Fokas system using two variables G′G,1G-expansion technique and generalized projective Riccati equation method

Research paper thumbnail of Implementation of the Exp-function approach for the solution of KdV equation with dual power law nonlinearity

Computational and Applied Mathematics

Research paper thumbnail of Bright, dark, periodic and kink solitary wave solutions of evolutionary Zoomeron equation

The modified auxiliary equation (MAE) approach and the generalized projective Riccati equation (G... more The modified auxiliary equation (MAE) approach and the generalized projective Riccati equation (GPRE) method are used to solve the Zoomeron problem in this study. Different types of exact traveling wave solutions are achieved, including solitary wave, periodic wave, bright, dark peakon, and kink-type wave solutions. Earned results are given as hyperbolic and trigonometric functions. Moreover, the dynamical features of obtained results are demonstrated through interesting plots.

Research paper thumbnail of Soliton formation to study the dynamical behaviour of biological evolution model

This article investigates the fractional Peyrard-Bishop DNA model. The construction of soliton so... more This article investigates the fractional Peyrard-Bishop DNA model. The construction of soliton solutions have been successfully obtained by utilizing two versatile analytical methods, namely, the Jacobi elliptic function method and the tanh-coth method. Furthermore, the Painlev´e test (P-test) has been employed on the proposed model for investigating integrability. The proposed model is proved to be integrable. Some of the obtained solutions have been examined graphically to study the dynamical behavior.

Research paper thumbnail of Analytical approximate solutions of time-fractional integro-differential equations using a new iterative technique

Research paper thumbnail of Soliton Dynamics of the Generalized Shallow Water Like Equation in Nonlinear Phenomenon

Frontiers in Physics, 2022

The generalized shallow water like equation is investigated in this research paper. Exact solutio... more The generalized shallow water like equation is investigated in this research paper. Exact solutions of generalized shallow water like equation are extracted using modified auxiliary equation (MAE) method and extended (G′G2)-expansion method. Many novel soliton solutions are obtained using these methods. The retrieved solution of governing model include rational, trigonometric and hyperbolic functions. The 3D graphs, 2D contour graphs and line graphs of obtained solutions are plotted using symbolic software such as Maple. The aim of plotting graphs is to demonstrate the dynamical behavior of acquired solutions. Thus, this study investigate the exact soliton solutions of generalized shallow water like using proposed methods.

Research paper thumbnail of An investigation of fractional complex Ginzburg–Landau equation with Kerr law nonlinearity in the sense of conformable, beta and M-truncated derivatives

Optical and Quantum Electronics, 2022

Research paper thumbnail of Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique

Fractal and Fractional, 2022

Developing mathematical models of fractional order for physical phenomena and constructing numeri... more Developing mathematical models of fractional order for physical phenomena and constructing numerical solutions for these models are crucial issues in mathematics, physics, and engineering. Higher order temporal fractional evolution problems (EPs) with Caputo’s derivative (CD) are numerically solved using a sextic polynomial spline technique (SPST). These equations are frequently applied in a wide variety of real-world applications, such as strain gradient elasticity, phase separation in binary mixtures, and modelling of thin beams and plates, all of which are key parts of mechanical engineering. The SPST can be used for space discretization, whereas the backward Euler formula can be used for time discretization. For the temporal discretization, the method’s convergence and stability are assessed. To show the accuracy and applicability of the proposed technique, numerical simulations are employed.

Research paper thumbnail of A comparative study of the optical solitons for the fractional complex Ginzburg–Landau equation using different fractional differential operators

Research paper thumbnail of The dynamical study of Biswas–Arshed equation via modified auxiliary equation method

Research paper thumbnail of Effects of fractional order derivative on the solution of time-fractional Cahn–Hilliard equation arising in digital image inpainting

Indian Journal of Physics, 2020

The Cahn–Hilliard equation is a nonlinear partial differential equation which is used in digital ... more The Cahn–Hilliard equation is a nonlinear partial differential equation which is used in digital image inpainting to restore damaged or missing parts of degraded text and high contrast images. Due to the nonlocal property of the fractional derivative, the fractional order Cahn–Hilliard equation can describe these physical processes in more flexible way. In this paper, the effects of fractional order derivative on the solutions of time-fractional Cahn–Hilliard equation are investigated using a new modification of the homotopy analysis method and a recently developed technique, namely residual power series method. The numerical and graphical illustrations depict the accuracy and reliability of the obtained results.

Research paper thumbnail of Observations of fractional effects of β-derivative and M-truncated derivative for space time fractional Phi-4 equation via two analytical techniques

Chaos, Solitons & Fractals

Research paper thumbnail of Soliton solutions of Lakshmanan-Porsezian-Daniel model using modified auxiliary equation method with parabolic and anti-cubic law of nonlinearities

Research paper thumbnail of Extraction of new exact soliton solutions and Painlevé-test for fractional Cahn–Allen equation

Optical and Quantum Electronics

Research paper thumbnail of Abundant optical solitons for Lakshmanan–Porsezian–Daniel model by the modified auxiliary equation method

Research paper thumbnail of Construction of new solutions of Korteweg-de Vries Caudrey-Dodd-Gibbon equation using two efficient integration methods

PLOS ONE, 2022

Korteweg-de Vries Caudrey-Dodd-Gibbon (KdV-CDG) equation describes many physical phenomena in pla... more Korteweg-de Vries Caudrey-Dodd-Gibbon (KdV-CDG) equation describes many physical phenomena in plasma physics, optical fibers, dynamics of the ocean, quantum mechanics, acoustic waves and laser optical applications. In this paper, the KdV-CDG equation is analyzed via two reliable and efficient integrating approaches. The suggested techniques; the extended G 0 G 2-expansion method and exponential (ψ(ξ))-expansion method successfully extract hyperbolic function solutions, trigonometric function solutions and rational function solutions. The existence criteria for all the obtained solutions are also discussed in this paper. At the end, various 3D and 2D contour plots have been constructed for better understanding of constructed solutions.

Research paper thumbnail of Extraction of new exact solutions of the resonant fractional nonlinear Schrödinger equation via two integrating techniques

Optical and Quantum Electronics

Research paper thumbnail of Dynamics investigation of the (4+1)-dimensional Fokas equation using two effective techniques

Research paper thumbnail of Optical soliton solutions of fractional Sasa-Satsuma equation with beta and conformable derivatives

Optical and Quantum Electronics

Research paper thumbnail of Optical solitons for the complex Ginzburg–Landau equation with Kerr law and non-Kerr law nonlinearity

Optical and Quantum Electronics

Research paper thumbnail of Exact soliton and solitary wave solutions to the Fokas system using two variables G′G,1G-expansion technique and generalized projective Riccati equation method

Research paper thumbnail of Implementation of the Exp-function approach for the solution of KdV equation with dual power law nonlinearity

Computational and Applied Mathematics

Research paper thumbnail of Bright, dark, periodic and kink solitary wave solutions of evolutionary Zoomeron equation

The modified auxiliary equation (MAE) approach and the generalized projective Riccati equation (G... more The modified auxiliary equation (MAE) approach and the generalized projective Riccati equation (GPRE) method are used to solve the Zoomeron problem in this study. Different types of exact traveling wave solutions are achieved, including solitary wave, periodic wave, bright, dark peakon, and kink-type wave solutions. Earned results are given as hyperbolic and trigonometric functions. Moreover, the dynamical features of obtained results are demonstrated through interesting plots.

Research paper thumbnail of Soliton formation to study the dynamical behaviour of biological evolution model

This article investigates the fractional Peyrard-Bishop DNA model. The construction of soliton so... more This article investigates the fractional Peyrard-Bishop DNA model. The construction of soliton solutions have been successfully obtained by utilizing two versatile analytical methods, namely, the Jacobi elliptic function method and the tanh-coth method. Furthermore, the Painlev´e test (P-test) has been employed on the proposed model for investigating integrability. The proposed model is proved to be integrable. Some of the obtained solutions have been examined graphically to study the dynamical behavior.

Research paper thumbnail of Analytical approximate solutions of time-fractional integro-differential equations using a new iterative technique

Research paper thumbnail of Soliton Dynamics of the Generalized Shallow Water Like Equation in Nonlinear Phenomenon

Frontiers in Physics, 2022

The generalized shallow water like equation is investigated in this research paper. Exact solutio... more The generalized shallow water like equation is investigated in this research paper. Exact solutions of generalized shallow water like equation are extracted using modified auxiliary equation (MAE) method and extended (G′G2)-expansion method. Many novel soliton solutions are obtained using these methods. The retrieved solution of governing model include rational, trigonometric and hyperbolic functions. The 3D graphs, 2D contour graphs and line graphs of obtained solutions are plotted using symbolic software such as Maple. The aim of plotting graphs is to demonstrate the dynamical behavior of acquired solutions. Thus, this study investigate the exact soliton solutions of generalized shallow water like using proposed methods.

Research paper thumbnail of An investigation of fractional complex Ginzburg–Landau equation with Kerr law nonlinearity in the sense of conformable, beta and M-truncated derivatives

Optical and Quantum Electronics, 2022

Research paper thumbnail of Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique

Fractal and Fractional, 2022

Developing mathematical models of fractional order for physical phenomena and constructing numeri... more Developing mathematical models of fractional order for physical phenomena and constructing numerical solutions for these models are crucial issues in mathematics, physics, and engineering. Higher order temporal fractional evolution problems (EPs) with Caputo’s derivative (CD) are numerically solved using a sextic polynomial spline technique (SPST). These equations are frequently applied in a wide variety of real-world applications, such as strain gradient elasticity, phase separation in binary mixtures, and modelling of thin beams and plates, all of which are key parts of mechanical engineering. The SPST can be used for space discretization, whereas the backward Euler formula can be used for time discretization. For the temporal discretization, the method’s convergence and stability are assessed. To show the accuracy and applicability of the proposed technique, numerical simulations are employed.

Research paper thumbnail of A comparative study of the optical solitons for the fractional complex Ginzburg–Landau equation using different fractional differential operators

Research paper thumbnail of The dynamical study of Biswas–Arshed equation via modified auxiliary equation method

Research paper thumbnail of Effects of fractional order derivative on the solution of time-fractional Cahn–Hilliard equation arising in digital image inpainting

Indian Journal of Physics, 2020

The Cahn–Hilliard equation is a nonlinear partial differential equation which is used in digital ... more The Cahn–Hilliard equation is a nonlinear partial differential equation which is used in digital image inpainting to restore damaged or missing parts of degraded text and high contrast images. Due to the nonlocal property of the fractional derivative, the fractional order Cahn–Hilliard equation can describe these physical processes in more flexible way. In this paper, the effects of fractional order derivative on the solutions of time-fractional Cahn–Hilliard equation are investigated using a new modification of the homotopy analysis method and a recently developed technique, namely residual power series method. The numerical and graphical illustrations depict the accuracy and reliability of the obtained results.

Research paper thumbnail of Observations of fractional effects of β-derivative and M-truncated derivative for space time fractional Phi-4 equation via two analytical techniques

Chaos, Solitons & Fractals

Research paper thumbnail of Soliton solutions of Lakshmanan-Porsezian-Daniel model using modified auxiliary equation method with parabolic and anti-cubic law of nonlinearities

Research paper thumbnail of Extraction of new exact soliton solutions and Painlevé-test for fractional Cahn–Allen equation

Optical and Quantum Electronics

Research paper thumbnail of Abundant optical solitons for Lakshmanan–Porsezian–Daniel model by the modified auxiliary equation method