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A novel computational approach to the local fractional Lonngren wave equation in fractal media
The main purpose of this paper is to investigate the local fractional Lonngren wave equation, which is a generalization of Lonngren wave equation in...
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Solitary waves of the fractal Whitham–Broer–Kaup equation in shallow water
In the current work, we propose the fractal Whitham–Broer–Kaup equation which can well describe the propagation of shallow water travelling along...
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Wave Profile, Paul-Painlevé Approaches and Phase Plane Analysis to the Generalized (3+1)-Dimensional Shallow Water Wave Model
In this paper, the solitary wave solutions, the periodic type, and single soliton solutions are acquired. Here, the Hirota bilinear operator is...
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Influence of the Free Parameters and Obtained Wave Solutions from CBS Equation
This manuscript investigates the exact travelling wave solutions of the (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. By...
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A new class of travelling wave solutions for local fractional diffusion differential equations
In this paper, we investigate a 3-D diffusion equation within the scope of the local fractional derivative. For this model, we establish local...
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An Approximate Solution Technique for the Flow Past an Obstacle with a Large Weber Number
The main objective of this work was to determine the shape of the two-dimensional free-surface flow over a triangular obstacle placed over a semi...
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On Fractional FitzHugh-Nagumo Equation as a Transmission of Nerve Impulses Design
This work apprises the exact solutions of the fractional Fitzhugh-Nagumo equation as a model of transmission of nerve impulses. Two methods via the...
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A Staggered Pressure Correction Numerical Scheme to Compute a Travelling Reactive Interface in a Partially Premixed Mixture
We address a turbulent deflagration model with a flow governed by the compositional Euler equations and the flame propagation represented by the...
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Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case
We study the large time behaviour of the solutions of a nonlocal regularisation of a scalar conservation law. This regularisation is given by a...
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New Optical Solitons for Time Fractional Coupled Zakharov Equations
Here, new methods called the exp a function and Kudryashov methods are implemented to obtain the analytical solutions of the fractional Zakharov...
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Real-time forecasting of the COVID 19 using fuzzy grey Markov: a different approach in decision-making
The ongoing epidemic SARS-CoV-2 named Corona Virus Disease (COVID-19) is highly infectious and subsequently spread all over the world affecting...
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Some More Invariant Solutions of (2 + 1)-Water Waves
In view of applicability of water waves, the objective of this article is to provide some more analytical solutions of (2 + 1)-dimensional water...
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A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion
Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells,...
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Taylor-Heat Flux Effect on Fluid Flow and Heat Transfer in a Curved Rectangular Duct with Rotation
A mathematical model is analyzed to study Taylor-heat flux effect on fluid flow and energy distribution through a curved duct (CD) of rectangular...
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Stanley Kubrick’s Perfection and the Divine Proportion
In cinematography, Stanley Kubrick is universally known as one of the most significant proponents. He experimented several cinematographic styles:...
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Asymptotic stability of traveling wave solutions for nonlocal viscous conservation laws with explicit decay rates
We consider scalar conservation laws with nonlocal diffusion of Riesz–Feller type such as the fractal Burgers equation. The existence of traveling...
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Separation variable method combined with integral bifurcation method for solving time-fractional reaction–diffusion models
In this paper, based on the previous works, we improve a computational method on solving time-fractional partial differential equation. Using the...
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Diverse Applications
The final chapter assembles a miscellany of applications, starting with various methods of data analysis, including statistical methods, phase space...
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Trajectory Dynamical Systems and Their Attractors
We start with the definition of Kolmogorov ε-entropy, via which we define fractal dimension of the compact set in the metric space. We will use these...