# Kottakkaran Sooppy NisarPrince Sattam bin Abdulaziz University · Department of Mathematics (Wadi Addawasir)

Kottakkaran Sooppy Nisar

Full Professor (M.Sc, M.Phil, Ph.D)

Mathematical Modelling; Fractional Calculus; Fluid Dynamics; Energy; Optimization Techniques; Special functions

## About

952

Publications

229,771

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Introduction

Prof (Dr) K. S. Nisar is working as a Full Professor at Prince Sattam bin Abdulaziz University, Saudi Arabia. His current research interests are Special functions, inequalities, Fractional Calculus, Fluid dynamics, Mathematical Modelling, Bio Mathematics, Fixed point theory and applications, SAC-OCDMA code networks, Activation of Energy, Artificial intelligence, Neural network, controllability and approximation, Machine Learning and interdisciplinary application of Mathematics.

Additional affiliations

November 2016 - present

November 2011 - October 2015

November 2011 - October 2015

Education

October 2008 - January 2011

## Publications

Publications (952)

In this paper we construct some positive linear operators by means of q-Lagrange polynomials and prove some approximation results via A-statistical convergence. We also define and study the rate of A-statistical approximation of these operators by using the notion of modulus of continuity and Lipschitz class.

In this manuscript, we develop existence, uniqueness and stability criteria for fractional-order Typhoid fever model having Caputo-Fabrizio operator by using fixed point theory. This approach of the fractional derivative is relatively new for such kind of biological models. We have also obtained the first accessible approximate solutions for a prop...

The new idea of Atangana and Baleanu introduced recently for fractional derivatives has received tremendous attention from researchers of various fields. However, this idea has not been applied for heat dissipation in transmission line of electrical circuit. Although the phenomenon of heat dissipation potentially damages the electrical devices whic...

In this work, we study a fractional extension of modified Kawahara equation by using Atangana–Baleanu fractional operator in the sense of Caputo (ABC). The fractional modified Kawahara equation is very useful to describe plasma waves and capillary-gravity water waves. We show existence and uniqueness of the solution of fractional modified Kawahara...

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking this into account, in the present work, we have analysed a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulat...

The two-dimensional radiating mixed convective flowing in a nanofluid, together with the non-Darcy penetrable material over an inclined wavy surface is examined. The conversion from the wavy surface into a smooth surface is performed, via coordinate transformation. The early stage of a mathematical formulation is converted into a group of ordinary...

Dispersive wave propagations are described by nonlinear models, such as regularized long waves and modified regularized long waves, where nonlinearity and dispersion are important aspects of wave evolution to model long-wave propagation in dispersive media with small amplitudes. In this article, solitary wave solutions to the formerly indicated non...

Controllability results of Hilfer delay fractional derivative(HDFD) with nondense operator have been articulated in this article. Primary discussions were made on the existence of mild solution using the Banach contraction principle and continued with controllability results by Darbo-Sadavoskii fixed point theorem. Obtained results enhanced via the...

A lot of numerical formulations of physical phenomena contain 9th-order BVPs. The presented probe intends to consider the spline solutions of the 9th-order boundary value problems using Cubic B Spline(CBS). Ninth order boundary value problems arise in the study of laminar viscous flow in a semi-porous channel, astrophysics, hydrodynamic & hydro-mag...

In this work, the influence of thermal energy in term of heat source, thermal radiation and chemical reaction on magneto hydrodynamic Casson fluid flow model (MHD-CFM) over a nonlinear slanted extending surface with slip velocity in a Forchheimer permeable medium is numerically studied using the Levenberg Marquardt methodology with backpropagated l...

The fractional calculus (FC) has been extensively studied by researchers due to its vast applications in sciences in the last few years. In fractional calculus, multivariate Mittag–Leffler functions are considered the powerful extension of the classical Mittag–Leffler functions. This paper defines the generalized fractional integral operator with m...

Non-ideal sampling has nourished as one of the most attractive alternatives to classical
sampling, which relies on shift-invariant spaces. The present study focuses on investigating the nonideal sampling in shift-invariant spaces associated with the quadratic-phase Fourier transforms. The primary aim is to formulate novel convolution structures in...

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for M...

The approximate controllability results of Atangana-Baleanu fractional stochastic inte-grodifferential systems with infinite delay are the topic of this paper. The essential discoveries are developed by employing techniques and theories from stochastic analysis, multivalued map theory, fractional calculus, and fixed point procedure. Before establis...

The foremost energy source originating from the sun, which is solar energy is widely utilized in solar technologies such as photovoltaic cells installed in energy plates, street lights, and water pumping. Meanwhile, the combination between solar radiations and nanotechnology is utilized in solar aircraft (SA). Therefore, this article investigated t...

It is critical to have precise data about Lithium-ion batteries, such as the State-of-Charge (SoC), to maintain a safe and consistent functioning of battery packs in energy storage systems of electric vehicles. Numerous strategies for estimating battery SoC, such as by including the coulomb counting and Kalman filter, have been established. As a re...

This work discovers the Laplace transform using a generalized pathway fractional integral formula involving an extended Mittag-Leffler function in the kernel for various parameters. Our findings are fairly broad in scope. Some well-known and novel results can also be obtained here.

The aim of the study is to discuss the controllability results of Hilfer neutral non-instantaneous impulsive fractional integro-differential equations (HNNIIFIE). Total controllability results were discussed by employing set-contraction theory and Kuratowski measure of non-compactness. Also we derived the results on optimal control using appropriat...

This manuscript investigates the issue of existence results for fractional differential evolution inclusions of order r ∈ (1, 2) in the Banach space. In the beginning, we analyze the existence results by referring to the fractional calculations, cosine families, multivalued function, and Martelli’s fixed point theorem. The result is also used to in...

In the study, the sudden act of the cancer model was studied utilizing the fractional operator and its applications to discretize the conformable cancer model. A collection of nonlinear fractional differential equations make up the fractional-order model. We also look at the fractional-order model, which examines how chemotherapeutic attention medi...

In this paper, we examine the multi-derivative nonlinear fractional integro-differential equations involving Atangana-Baleanu fractional derivative of Riemann-Liouville sense. We study the elementary results about the existence and difference solution on different data, based on T. R. Prabhakar fractional integral operator εσ,η,ϑ;c+γ involving gene...

In this article, we investigate the mechanics of breathing performed by a ventilator with different kernels by an effective integral transform. We mainly obtain the solutions of the fractional respiratory mechanics model. Our goal is to give the underlying model flexibly by making use of the advantages of the non-integer order operators. The big ad...

The study of approximate controllability results ensures the essential conditions required for a solution. Keeping the importance of the study, we initiate the existence and approximate controllability an Atangana-Baleanu-Caputo (ABC)-fractional order neutral delay integrodifferential stochastic systems with nonlocal conditions. For this purpose, t...

In this article, radial basis function (RBFs) based, the mesh-less method is suggested to study non-linear Foam Drainage and Fractional Foam Drainage Equations. For this purpose, θ-weighted scheme is implemented along with the quasi-linearization technique on the spatial part to linearize the non-linear terms. Finite difference along with Crank-Nic...

In this article, a mathematical model of the COVID-19 pandemic with control parameters is introduced. The main objective of this study is to determine the most effective model for predicting the transmission dynamic of COVID-19 using a deterministic model with control variables. For this purpose, we introduce three control variables to reduce the n...

This study emphasizes the performance of two-dimensional electrically non-conducting Oldroyd-B fluid flowing across a stretching sheet with thermophoretic particle deposition. The heat and mass transfer mechanisms are elaborated in the presence of a magnetic dipole, which acts as an external magnetic field. The fluid possesses magnetic characterist...

The article uses semigroup theory and Gronwall's inequality to investigate the approximate controllability of impulsive semilinear control systems. A weaker Lipschitz condition on non-linearity is enforced to reach the main conclusions. Two sets of assumptions have been used to discuss the key findings. As noted before by various researchers in the...

In present research manuscript, analysis is presented for the influences of heat transition in a bodewadt flow over a penetrable disk numerically. Estimation parameters in current mathematical flow model include magnetic field parameter (0.1≤M≤1.2), wall suction (1.7≤A≤6.7), prandtl number (0.2≤Pr≤5.0), heat generation/absorption (-0.9≤Q≤3.6), ecke...

This article discusses the stability of a two-species ecosystem composed of an ammensal (x) and an adversarial (y) species that are continuously harvested. A mathematical model is defined by a system of two nonlinear ordinary differential equations of first order. The considered system's boundedness is investigated. The local stability of the syste...

This work establishes the existence and uniqueness (EUS) of solutions for impulsive neutral mixed integro fractional delay differential equations involving recently explored ABC-fractional derivatives. Fixed-point techniques are applied to confirm EUS of solutions of ABC-fractional order integrodifferential system with impulse.

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature...

The use of hybrid nanoparticles to improve thermal processes is a key method that has implications for a variety of interventions utilized in many sectors. This paper aimed to look into the impacts of ternary nanoparticles on hyperbolic tangent materials to establish their thermal characteristics. Flow describing equations have been explored in the...

In this article we observed the Darcy-Brinkman flow model in the existence of frictional heating and porous dissipation (DBFM) over a stretching sheet by employ the neural network backpropagated with Bayesian regularization technique (NNBP-BRT). NNBP-BRT has the ability to exhibit relatively complex relationships, which implies it can be used in nu...

The major purpose of this article is to exploit the strength of the Intelligent Back-propagated Neural Networks of Levenberg Marquardt Technique (IBNN-LMT) to study three-dimensional (3D) squeezed flow model of carbon nanotubes (SFM-CNTs) relying on water in a revolving network with a rigid ground wall. The impact of magnetohydrodynamic (MHD) and t...

In this paper, we investigate the approximate controllability for fractional integrodifferential inclusions of order r∈(1,2) in Banach space with sectorial operators. In particular, we obtain a new set of sufficient conditions for the approximate controllability of nonlinear fractional integrodifferential inclusions of order r∈(1,2) under the assum...

The main focus of this manuscript is centered around Atangana-Baleanu semilinear fractional integro-differential equations with finite delay. The outcomes are demonstrated using the M\“onch fixed point theorem along with its results when the measure of noncompactness collaborates. Eventually, a demonstration example is proposed.

This paper presents an innovative artificial neural networks (ANNs) based hybrid algorithm of genetics optimization and sequential quadratic programming (AGOSQP) to construct the mathematical model for the dynamics of Lassa fever (DLF) in Nigeria. The model designated by the transmission of disease between two populations: human population i.e. sus...

The aim of this study is to investigate the numerical analysis of an innovative model containing, bioconvection phenomena with a gyrotactic motile microorganism of magnetohydrodynamics Williamson nanofluids flow along with heat and mass transfer past a stretched surface. The effect of thickness variation and thermal conductivity feature is employed...

Friction welding is a method of joining two materials in solid-state that have a good bonding connection. The materials are eventually joined by continuous acts of forging pressure combined with rotational drives by varying parameters such as friction pressure, forging pressure, friction time, rotation speed and upset time. Low input heat and high...

In this paper, we analyze the behavior of the neutral integro-differential equations of fractional order including the Caputo-Hadamard fractional derivative. The results and solutions are obtained using the topological degree method. Furthermore, some specific numerical examples are given to ascertain the wide applicability and high efficiency of t...

The mathematical modeling of hybrid nanofluid flow and heat transfer with entropy generation toward parabolic trough surface collector (PTSC) inside the solar-powered ship (SPS) is performed. The mathematical model used non-Newtonian Oldroyd-B model amidst a constant inclined magnetic field influence is being considered. The mathematical model is t...

The present works focus on the effects of electric and magnetic fields on the flow of micro-polar nano-fluid between two parallel plates with rotation under the impact of Hall current (EMMN-PPRH) has considered by using Artificial Neural Networks with the scheme of Levenberg-Marquardt backpropagation (ANN-SLMB). The nonlinear PDEs are transformed i...

In recent years, integral inequalities are investigated due to their extensive applications in several domains. The aim of the paper is to investigate certain new fractional integral inequalities which include Hermite-Hadamard inequality and different forms of trapezoid type inequalities related to Hermite-Hadamard inequality for h-Godunova-Levin p...

With the advent of the Internet of Things (IoT), its uses have been growing enormously in the smart healthcare sector. IoT devices in smart healthcare range from simple wristband devices capable of monitoring the heart rate, sleep pattern, and blood pressure to connected inhalers, ingestible sensors, glucose monitoring, and remote patient monitorin...

This study introduces a new continuous time differential system , which contains ten terms with three quadratic nonlinearities. The new system can demonstrate hyperchaotic, chaotic, quasi-periodic, and periodic behaviors for its different parameter values. All theoretical and numerical analysis are investigated to confirm the complex hyperchaotic b...

In this article, a novel collocation method is developed based on Gegenbauer wavelets together with the quasi-linearization technique to facilitate the solution of population growth model of fractional order in a closed system. The operational matrices of fractional order integration are obtained via block-pulse functions. The obtained matrices are...

The purpose of study is to present a new nanofluidic model and its solution that describes steady couple stress magnetic Casson nanofluid flow in the presence of Cattaneo-Christov heat flux (CMCN-CCHF) system past a shrinking plat via aesthetics stochastic computing procedure based on supervised learning Lavenberg-Marquard technique as a backpropag...

The population dynamics of two species that is governed by the deterministic Lotka-Volterra model concerned with the interaction of predator and prey is investigated in this article as an application of homotopy analysis method. The analytical approximate solution in the form of convergent infinite series is obtained by considering the time-fractio...

By taking variable temperature, we consider an MHD boundary layer flow past a flat plate with radiation, joule heating, and viscous dissipation effects. The suitable similarity transformation is used to obtain ODEs from governing non-linear coupled PDEs, which are solved by the engaging shooting method. The mechanical energy is converted to thermal...

It is well known that solar energy is the main source of thermal energy coming from the sun responsible for huge operations in engineering studies. It can be seen in the technology of photovoltaic cells, solar streetlights, solar energy plates, and solar water pumping. This study is for investigating solar radiation as well as a method to improve t...

This paper deals with the existence and approximate controllability outcomes for Hilfer fractional neutral evolution equations. To begin, we explore existence outcomes using fractional computations and Banach contraction fixed point theorem. In addition, we illustrate that a neutral system with a time delay exists. Further, we prove the considered...

This paper is devoted to studying the approximate controllability for second-order impulsive differential inclusions with infinite delay. For proving the main results, we use the results related to the cosine and sine function of operators, Martelli’s fixed point theorem, and the results when combined with the properties of differential inclusions....

The main purpose of this work is to investigate the influence of multi slip implications on steady-state MHD fluid flow in the occurrence of Soret and Dufour through a suction/ injection over a non-Isothermal stretching surface. The governing equations are converted into non-linear ODEs using similarity variables. The Keller box technique is used t...

In this work, we analyse the study of neutral fractional differential equation in an arbitrary Hilbert space. An associated integral equation is studied and approximate integral equation is obtained. We demonstrate the existence and uniqueness of an approximate solution by using analytic semigroup theory and the Fixed point method. In the applicati...

The present study is influenced by the wide applications of the Schrödinger equations. Its occurrence can be easily seen in electromagnetic wave propagation, quantum mechanics, plasma physics, nonlinear optics, underwater acoustics, etc. Solving equations of this type is always difficult. In the current paper, we have discussed a very easy numerica...

The purpose of this paper is to explore the behavior of Sutterby nanofluid passed a sloping sheet with a tendency to fluctuate thermal conductivity, radiation and a magnetic field. In a solar parabolic trough collector (PTC) for solar cooling and hydrogen generation, a nanofluid is employed as the running fluid. The Koo-Kleinstreuer-Li (KKL) model...

In this article, the generalized $ \left(N+1\right) $-dimensional nonlinear Boussinesq equation is analyzed via Lie symmetry method. Lie point symmetries of the considered equation and accompanying invariant groups are computed. After transforming the equation into a nonlinear ordinary differential equation (ODE), analytical solutions of various ty...

In this paper, an efficient technique called Optimal Homotopy Asymptotic Method has been extended for the first time to the solution of the system of fuzzy integro-differential equations of fractional order. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a conv...

In this chapter, we establish some existence of solutions for 2D functional integral equations concerning Darbo’s fixed point theorem in Banach algebra. This existence of solutions involves various obtained from earlier studies. Some examples are introduced to confirm the applicability of our results.

In this paper, by applying Pachpatte’s type integral inequality with integral impulses, we investigate Ulam–Hyers and Ulam–Hyers–Rassias stabilities for the impulsive Volterra delay integrodifferential equation Banach spaces. Suitable examples are given to support the obtained results.

This study investigates the functional abstract second order impulsive differential equation with state-dependent delay. The major result of this study is that the abstract second-order impulsive differential equation with state-dependent delay system has at least one solution and is unique. After that, the wellposed condition is defined. Following...

In this study, we investigate differential and integral equations of some hybrid families of truncated exponential-based Sheffer polynomials. We also derive some integro-differential equation and new recurrence relations for the truncated exponential based Sheffer polynomials by using the factorization method. We also discuss some special cases as...

In this article, we investigate existence and the exact solutions of the extended Fisher-Kolmogorov (EFK) equation. This equation is used in the population growth dynamics and wave propagation. The fourth-order term in this model describes the phase transitions near critical points which are also known as Lipschitz points. He's variational method i...

This article is primarily targeting the approximate controllability results of Atangana-Baleanu neutral fractional stochastic hemivariational inequality. The primary conclusions were validated using principles and ideas from stochastic analysis, fractional calculus, multivalued map theory, and fixed point techniques. We begin by emphasizing the exi...

The main focus of this paper is on the boundary controllability of fractional order Sobolev-type neutral evolution equations in Banach space. We show our key results using facts from fractional calculus, semigroup theory, and the fixed point method. Finally, we give an example to illustrate the theory we have established.

The main focus of this paper is on the boundary controllability of fractional order Sobolev type neutral evolution equations in Banach space. We show our key results using facts from fractional calculus, semigroup theory, and the fixed point method. Finally, we give an example to illustrate the
theory we have established.

In this paper, we investigate the approximate controllability results of Atangana-Baleanu fractional neutral stochastic systems with infinite delay. Using principles and ideas from stochastic analysis, the theory of multivalued maps, fractional calculus, and Bohnenblust-Karlin fixed point theorem, a new set of sufficient conditions are formulated a...

In this framework entropy generation optimization in dissipative flow of Ree-Eyring fluid model (EGODF-RFM) with chemical reaction of quartic autocatalysis between two rotating disks is observed by operating the artificial neural networks model backpropagated with Bayesian Regularization technique (ANNM-BBRT). The effects of viscous dissipation and...

The current emergence of coronavirus (SARS-CoV-2 or COVID-19) has put the world in threat. Social distancing, quarantine, governmental measures namely lockdowns, social isolation, and
public hygiene etc. are helpful in fighting the pandemic, while awareness campaigns through social
media (radio, TV etc.) are essential for their implementation. On...

Improving high-efficiency thermal systems to increase heat transmission has become quite prevalent nowadays. Various works were conducted to gain insight into the implementation of heat transfer for their practical use in increasing heat transfer. Therefore, the present study focuses on analyzing heat exchange and irreversibility rate (entropy gene...

The article analyzes the existence of Caputo fractional evolution integrodifferential equations of order 1 < r < 2 in Hilbert space with delay. A new set of adequate requirements for the existence outcomes of fractional delay evolution integrodifferential equations have been developed and are shown using the fractional derivative, Krasnoselskii's f...