Muhammad Sajid Iqbal

Oryx Universal College (LJMU) Doha Qatar & MCS (NUST) Islamabad Pakistan. · Foundation Studies & Mathematics

Starting from distinguishing boundaries for monogenic functions (see Tutschke in Adv. Appl. Clifford Algebr 25:441–451, 2015), one can solve boundary value problems for monogenic functions (see Dao in Boundary value problems for monogenic functions in higher dimensions. Ph.D Thesis, Hanoi University of Science and Technology, Vietnam, 2019). A boun...

The current article deals with the analysis and numerical solution of fractional order Schnakenberg (S-B) model. This model is a system of autocatalytic reactions by nature, which arises in many biological systems. This study is aiming at investigating the behavior of natural phenomena with a more realistic and practical approach. The solutions are...

Background and objective: Epidemic models are used to describe the dynamics of population densities or population sizes under suitable physical conditions. In view that population densities and sizes cannot take on negative values, the positive character of those quantities is an important feature that must be taken into account both analytically...

This paper presents an innovative collocation algorithm designed to effectively handle a specific class of boundary value problems with high-order characteristics. The approach involves utilizing a novel variant of exponential-type Chebyshev polynomials that meet all the necessary equation conditions. A key aspect of the algorithm is the transforma...

In this study, we investigated an allelopathic phytoplankton competition model under the effect of Brownian motion. This model is analyzed for the first time analytically to obtain the solitary wave solution, numerical results, and mainly their comparisons. The solitary wave solutions are constructed by using the \(\phi ^6\)-model expansion method...

In this paper, we investigate the optimal conditions to the boundaries where the unique existence of the solutions to an advection-diffusion-reaction equation is secured by applying the contraction mapping theorem from the study of fixed points. Also, we extract, traveling wave solutions of the underlying equation. To this purpose, a new extended d...

This work examines the (2+1)-dimensional Boiti–Leon–Pempinelli model, which finds its use in hydrodynamics. This model explains how water waves vary over time in hydrodynamics. We provide new explicit solutions to the generalized (2+1)-dimensional Boiti–Leon–Pempinelli equation by applying the Sardar sub-equation technique. This method is shown to...

This study introduces a fractional order model to investigate the dynamics of polio disease spread, focusing on its significance, unique results, and conclusions. We emphasize the importance of understanding polio transmission dynamics and propose a novel approach using a fractional order model with an exponential decay kernel. Through rigorous ana...

Prey and predator are the important factor of the ecosystem. Generally, it is considered that prey-predator models depends on time and it is only required nonlinear system of equations for its dynamical study. But it is observed that such species can move from one to place to another and in such a way there is a need of nonlinear equations which al...

This manuscript studies the exact solitary wave profiles for the conformable Schrödinger–Poisson dynamical system. This system has a significant role in gravity’s quantum state operation approximates the interaction between quantum mechanics and gravitation. The diverse exact solitary wave profiles are constructed by using the Khater method. The di...

This study deals with the time fractional 1D stochastic Poisson–Nernst–Planck (TFSPNP) system under the effect of multiplicative time noise. The M-truncated derivative (MTD) takes into consideration the fractional order time derivative. This is a steady-state Poisson–Nernst–Planck (PNP) equations that have applications in bioelectric dressings and...

In this manuscript, we investigates the stochastic Davey–Stewartson equation under the influence of noise in Ito^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{o...

In this research article, we apply the generalized projective Riccati equation method to construct traveling wave solutions of the 3d cubic focusing nonlinear Schrodinger equation with Woods-Saxon potential. The generalized projective Riccati equation method is a powerful and effective mathematical tool for obtaining exact solutions of nonlinear pa...

This study proposed a modified G′/G2 -expansion method to seek the new exact traveling wave solutions of the Newell–White–Head–Segel (NWHS) Model. This is an amplitude equation utilized for distributing temperature within a rod that is infinitely thin and long, or determining the flow velocity of a fluid through a pipe that is infinitely long but h...

The design of computer modelling has a vital role in the recent development of scientific literature. Creation, modification, analysis, and optimization of structures are uses of computer methods. The most significant benefit is communication through documentation, quality of design, designing electronic systems, and many more. According to the Wor...

The Biswas–Mollivic equation is a special type of nonlinear Schrödinger equation, which explains the spatio-temporal behaviour of excitable media. In this paper, we investigate the optical soliton solutions of the Biswas–Mollivic equation with cubic–quintic–septic–nonic nonlinearities using the generalized Riccati equation mapping method. This meth...

In this study, the stochastic Chen–Lee–Liu equation is considered numerically and analytically which is forced by the multiplicative noise in the Itô sense. The Chen–Lee–Liu equation is a special type of Schrödinger’s equation which has applications in optical fibers and photonic crystal fibers. The stochastic Crank–Nicolson scheme is formed to obt...

In this manuscript, the well-known stochastic Burgers’ equation in under investigation numerically and analytically. The stochastic Burgers’ equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This study is presented the existence, approximate, and exact...

This study deals with the stochastic Fitz-Hugh Nagumo (FHN) equation and its multiple soliton solutions. The underlying model has numerous applications in neuroscience that express the pulse behavior of neurons. In general, different kinds of noise affect neurons, e.g., oscillations in the opening and closing of ion stations within cell membranes a...

Solitary wave solutions are of great interest to bio-mathematicians and other scientists because they provide a basic description of nonlinear phenomena with many practical applications. They provide a strong foundation for the development of novel biological and medical models and therapies because of their remarkable behavior and persistence. The...

This study deals with a stochastic reaction-diffusion biofilm model under quorum sensing. Quorum sensing is a process of communication between cells that permits bacterial communication about cell density and alterations in gene expression. This model produces two results: the bacterial concentration, which over time demonstrates the development an...

In this research article, we analyzed the fractional order Selkov-Schnakenberg system under consideration for the sake of classical regularity and analytical solutions. The existence and uniqueness of the solution of this fractional system were evaluated using self-mapping, contraction mapping, and Schauder fixed point conditions from fixed point t...

The (3+1)-dimensional double sine-Gordon equation plays a crucial role in various physical phenomena, including nonlinear wave propagation, field theory, and condensed matter physics. However, obtaining exact solutions to this equation faces significant challenges. In this article, we successfully employ a modified $$ \left( \dfrac{G'}{G^2}\right)...

In this manuscript, the soliton structures for the time-fractional KdV–Burgers–Fisher equation with the effect of noise are investigated analytically. This is the dispersion–dissipation–reaction model. The third- and fifth-order time-fractional stochastic KdV–Burgers–Fisher equations are under consideration. These wave structures are constructed wi...

In this study, the optimization of the fixed point in function spaces and exact solutions to the biofilm model are studied to describe growth, and bacteria working together, including quorum sensing. Engineering applications that involve biotechnology, environmental engineering, and the creation of medical devices are particularly pertinent to biof...

In this paper, the exact solutions of classical and stochastic Maccari system is constructed. The exact comparative solutions are examined and plotted. Interesting results in the case of multiplicative noise are formulated and graphically elaborated. The applications of the stochastic Maccari system are added for the physical purpose. The existence...

In this paper the major work is done on the optimal solution of f(R, T) gravity 00-component field equation. Explicit derivation of 00 and 11-components has been done. Optimal existence of solution of 00-component has been formulated using fixed point theory. The equivalence of 00-component of f(R, T) gravity field equation with wave equation havin...

In this article, the two-dimensional time fractional unsteady convection-diffusion system is under consideration. The convection-diffusion system of nonlinear partial differential equations has remained a uniform fascination for scientists owing to its energetic significance as well as its possession of a broad spectrum of practical and physical ap...

In this manuscript, the Sobolev-type equations are examined analytically. The Sobolev-type equations are important in many fields, including thermodynamics, physics, soil mechanics, fluid flow through fissured rock sand, shear in second-order fluids, and mechanical engineering. We have looked into two dynamical systems involving Sobolev type nonlin...

An essential stage in the spread of cancer is the entry of malignant cells into the bloodstream. The fundamental mechanism of cancer cell intravasation is still completely unclear, despite substantial advancements in observing tumor cell mobility in vivo. By creating therapeutic methods in conjunction with control engineering or by using the models...

In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction–diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor chlorite and the activator iodide are shown in the form of wave solutions. This is a reaction†“dif...

Ecological system is the interaction of biological community with other organisms and to their physical environments. One of the important model is spatiotemporal prey-predator model of Michaelis Menten–type functional response and reaction diffusion with constant harvest rate. This paper investigates the spatiotemporal structures of ratio-dependen...

In the present work, Einstein's vacuum field equation is investigated analytically to explore the solitary wave solutions. This equation arises in mathematical physics, having meaningful applications in the general theory of relativity. This concept is crucial for numerous challenging experiments and space missions. The generalized exponential rati...

This manuscript presents the stability analysis of the diarrhea epidemic model with the effect of time delay. The delayed epidemic model for the disease of diarrhea contains four compartments, including susceptible, infective, treated, and recovered classes. The artificial delay parameter is designed with a saturated incidence rate of the model. Th...

In this study, the propagation of the ultra-short femtosecond pulses in an optical fiber is modeled by the Kundu–Eckhaus equation with cubic, quintic nonlinearities, and the Raman effect. The Kundu–Eckhaus equation is a special class of nonlinear Schrödinger equation. To find optical soliton solutions, the extended generalised Riccati equation mapp...

This study investigates a stochastic nonlinear Schrödinger equation (1+1) dimensional with a random potential. The equation under consideration is crucial in the study of the evolution of nonlinear dispersive waves in a completely disordered medium. By employing the ϕ6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepacka...

Solitons are characterized by their ability to maintain their shape and velocity as they propagate through a medium, and are also known for their stability against mutual collisions. However, it is crucial to investigate the behavior of nonlinear partial differential equations under random environmental conditions, as this has important implication...

In this study, the acoustic nonlinear equation namely the confirmable time-fractional Westervelt equation is under consideration analytically. This equation is applicable in the wave propagation of sound and high amplitude in medical imaging and therapy. The different types of wave structures are constructed for the confirmable time-fractional West...

The current study deals with the stochastic reaction–diffusion epidemic model numerically with two proposed schemes. Such models have many applications in the disease dynamics of wildlife, human life, and others. During the last decade, it is observed that the epidemic models cannot predict the accurate behavior of infectious diseases. The empirica...

In this paper, the examination of soliton solutions of the biofilm model with the help of a new extended direct algebraic method is expressed. Besides the exact solutions, the existence of these solutions is also discussed with the help of the Schauder fixed point theorem. The nonlinear dynamical biofilm model which we consider in this paper is bas...

In this research, the nonlinear mathematical model for enzyme-catalyzed reaction–diffusion phenomena has been analyzed for the exact solutions investigated analytically. As a result, it is critical to investigate this concept from a mathematical standpoint. The ϕ6-model expansion method is used to extract the analytical solutions which give the che...

In this article, families of solitary waves solutions of a general third-order nonlinear non-ohmic cable equation in cardio-electro-physiology are obtained using the $\exp(-\varphi(\xi))$-expansion method. In this equation, the unknown function represents the transmembrane current, and the exact soliton-like solutions are thoroughly derived using t...

This study presents the investigations on the effect of heat transfer on droplet formation in T-type microfluidic channel. Mineral oil acts as a continuous phase, and water acts as a dispersed phase. The Volume of Fluid model is used to investigate the formation of droplets of water in oil in the microchannel. The physical properties of both fluids...

The existence of solutions of coupled system of bi-harmonic Schrödinger equations as fixed point of an operator has been given in this article. The corresponding estimates for the length of continuity of solutions have been constructed. By applying new ϕ6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...

In this study, we construct the abundant families of soliton solutions for the generalized (2+1)-dimensional Camassa–Holm–KP equation. This equation is used in tiny amplitude shallow water waves. The solutions are obtained in the form of Jacobi elliptic function solutions which are the soliton and solitary wave solutions. They are observed in the f...

The current study deals with the stochastic Nizhnik–Novikov–Veselov (SNNV) system analytically under the multiplicative noise effect. The Nizhnik–Novikov–Veselov equation is an extension of the KdV equation with applications in shallow-water waves, ionic acoustic waves in plasma, long internal waves in density-stratified oceans, and sound waves on...

The stochastic Newell–Whitehead–Segel in (2+1) dimensions is under consideration. It represents the population density or dimensionless temperature and it discusses how stripes appear in temporal and spatial dimensional systems. The Newell–Whitehead–Segel equation (NWSE) has applications in different areas such as ecology, chemical, mechanical, bio...

In this paper, we investigate the soliton solutions of the time–space fractional order nonclassical Sobolev-type (TSFNST) equation. Sobolev equations are used in thermodynamics, the flow of fluid through fractured rock, and other fields. There are certain significant partial differential equations having a third-order mixed derivative with regard t...

In this article, the ratio-dependent prey-predator system perturbed with time noise is numerically investigated. It relates to the population densities of the prey and predator in an ecological system. The initial prey-predator models only depend on the time and a couple of the differential equations. We are considering a model where the prey-preda...

In this article, the stochastic Phi-4 model is under consideration analytically. The stochastic Phi-4 equation has been crucial to nuclear and particle physics. The randomness of the nuclear particle at the micro level is represented by the stochastic phenomena which are shown by the white noise. The stochastic version of the Phi-4 model is investi...

In this article, the transmission dynamical model of the deadly infectious disease named Ebola is investigated. This disease originated in the Democratic Republic of Congo (DRC) and Sudan (now South Sudan) and was identified in 1976. The novelty of the model under discussion is the inclusion of advection and diffusion in each compartmental equation...

The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates f...

In this article, a nonlinear autocatalytic chemical reaction glycolysis model with the appearance of advection and diffusion is proposed. The occurrence and unicity of the solutions in Banach spaces are investigated. The solutions to these types of models are obtained by the optimization of the closed and convex subsets of the function space. Expli...

In this study, the Gross–Pitaevskii equation perturbed with multiplicative time noise is under consideration numerically and analytically. The NLSE is a universal governing model that helps in evolution of complex fields that are used in dispersive media. For the numerical solution, we used the stochastic forward Euler (SFE) scheme. To find the exa...

In this study, the Gross–Pitaevskii equation perturbed with multiplicative time noise is under consideration numerically and analytically. The NLSE is a universal governing model that helps in evolution of complex fields that are used in dispersive media. For the numerical solution, we used the stochastic forward Euler (SFE) scheme. To find the exa...

In this article, stochastic behavior of reaction diffusion brusselator model is under consideration. There are many physical phenomena which are related to chemical concentrations. One chemical concentration coincide with the other chemical concentration and their inter-diffusion is a major question to be addressed and to be understood. So, that is...

Gutman and Trinajstic deducted that total π-energy of a chemical molecule depends upon a numeric value which is termed as zagreb index. In that same report, they also defined a term for a particular atom with respect to other atom which is away from at a distance two. This quantity provides π-energy for a molecule. Now a days, in subject context, t...