Mohammed K A Kaabar

Mohammed K A Kaabar
Washington State University | WSU · Department of Mathematics

(B.S+M.S+PhD (AMS Erdős Number=4) Research in Theoretical and Applied Mathematics) ✅ from WSU + Senior Member (Hong Kong Chemical, Biological & Environmental Engineering Society (HKCBEES) and International Engineering and Technology Institute)
Fractional Calculus; Computation; Numerical Analysis; Applied Analysis; Deep Learning; Networks; AI; Machine Learning

About

269
Publications
110,164
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870
Citations
Introduction
Mohammed Kaabar received his undergraduate and graduate degrees in Mathematics from Washington State University, Pullman, WA, United States. He worked as an Adjunct Professor of Mathematics at Moreno Valley College, CA, USA. He is an appointed math editorial board member for MERLOT II at California State University, Long Beach, CA, USA. He studied through distance education programs several STEM and leadership courses offered by Harvard University, MIT, École Polytechnique Fédérale de Lausanne, University of Michigan, UC Berkeley, University of Toronto, University of Rochester, and University of British Colombia. He is currently working in the area of Fractional Calculus, Fractional Differential Equations, Numerical Methods for Fractional Differential Equations, and Mathematical Modeling.
Additional affiliations
August 2016 - December 2016
Riverside Community College District
Position
  • Professor
Description
  • I worked as full math instructor for two sections of Elementary Algebra classes at Moreno Valley Location of RCCD.
August 2014 - present
Washington State University
Position
  • Research Assistant
Description
  • 1- Teaching Assistant of MATH 202. 2- Math Tutor at Math Learning Center (MLC) at Washington State University, Pullman.
August 2013 - January 2014
Washington State University
Position
  • Research Assistant
Description
  • 1- Teaching Assistant of MATH 201. 2- Math Tutor at Math Learning Center (MLC) at Washington State University, Pullman.
Education
February 2015 - May 2016
Washington State University
Field of study
  • PhD Student in Applied Mathematics
January 2015 - December 2018
Washington State University
Field of study
  • Applied Mathematics
August 2013 - December 2014
Washington State University
Field of study
  • Theoretical Mathematics

Publications

Publications (269)
Article
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Crimean-Congo hemorrhagic fever is a common disease between humans and animals that is transmitted to humans through infected ticks, contact with infected animals, and infected humans. In this paper, we present a boxed model for the transmission of Crimean-Congo fever virus. With the help of the fixed-point theory, our proposed system model is inve...
Article
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In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, a...
Article
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In this work, the (3+1)-dimensional Wazwaz–Benjamin–Bona–Mahony equation is formulated in the sense of conformable derivative. Two novel methods of generalized Kudryashov and expð−φðℵÞÞ are investigated to obtain various exact soliton solutions. All algebraic computations are done with the help of the Maple software. Graphical representations are p...
Article
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Our main purpose in this paper is to prove the existence of solutions for the fractionalstrongly singular thermostat model under some generalized boundary conditions. In this way, weuse some recent nonlinear fixed-point techniques involvingα-ψ-contractions andα-admissible maps.Further, we establish the similar results for the hybrid version of the...
Article
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A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function expanded by a Taylor series, we show that $D^{\alpha}D^{\beta}f(t)=D^{\alpha+\beta}f(t);0<\alpha\leq1$;$0<\beta\leq1$. GFD is applied for some functions to investigate that GFD coincides with the results from Caputo and Riemann-Liouville fra...
Article
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This article discusses the stability results for solution of a fractional q-integro-differential problem via integral conditions. Utilizing the Krasnoselskii’s, Banach fixed point theorems, we demonstrate existence and uniqueness results. Based on the results obtained, conditions are provided to ensure the generalized Ulam and Ulam–Hyers–Rassias st...
Article
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We have analyzed the two coupled nonlinear Schrödinger equations (CNLSE) in the current work. This model has applications in high birefringence fibers. To generate different types of analytical solutions, including exponential, periodic, and soliton-type, we operated generalized Kudryashov, modified Kudryashov and exponential rational function proc...
Preprint
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Abu-shady and Kaabar proposed a generalized fractional derivative (GFD) formulation [13], which produces satisfactory results that are consistent with conventional fractional derivative definitions such as Caputo (CP) and Riemann-Liouville (RL). To derive the fractional forms of special functions, GFD is used. The …ndings demonstrate that the curre...
Article
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Due to the size constraint, antennas with compact size are required that can support multibands with single radiating element. Dielectric Resonator Antenna (DRA) can support multiple modes with good efficiency and gain using single radiating element. In this paper, a quad-band DRA is proposed for WLAN/WiMAX bands using a single CPW feed. Out of fou...
Article
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The range of effectiveness of the novel corona virus, known as COVID-19, has been continuously spread worldwide with the severity of associated disease and effective variation in the rate of contact. This paper investigates the COVID-19 virus dynamics among the human population with the prediction of the size of epidemic and spreading time. Corona...
Article
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This article aims to develop a mathematical simulation of the steady mixed convective Darcy–Forchheimer flow of Williamson nanofluid over a linear stretchable surface. In addition, the effects of Cattaneo–Christov heat and mass flux, Brownian motion, activation energy, and thermophoresis are also studied. The novel aspect of this study is that it i...
Article
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An extended method of semidiscrete high-resolution finite volume is used in this paper to obtain numerical solutions for a formulated nonlinear lumped kinetic model of liquid chromatographic process to examine the effect of chromatographic column overloading gradient elution considering core-shell particles. The model constitutes linear solvent str...
Poster
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I am now serving as a section editor for the IETI Transactions on Data Analysis and Forecasting (iTDAF) (No APC (Free)). The journal is intended to publish manuscripts in all aspects of data analysis and forecasting. All researchers are very welcome to submit their high-quality papers to our journal. We will also offer awards to the highest quality...
Article
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SARS-CoV-2, known as COVID-19, has affected the entire world, resulting in an unexpected death rate as compared to the death probability before the pandemic. Prior to the COVID-19 pandemic, death probability has been assessed in a normal context that is different from those anticipated during the pandemic, particularly for the older population clus...
Article
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The existence aspects along with the stability of solutions to a Hadamard variable order fractional boundary value problem are investigated in this research study. Our results are obtained via generalized intervals and piecewise constant functions and the relevant Green function, by converting the existing Hadamard variable order fractional boundar...
Article
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is article studies the existence theory of an innovation type of generalized proportional fractional di erential equations with the assistance of the technique of Kuratowski measure on noncompactness combined with the xed-point theorem of Mönch. Also, we use Lebesgue's dominated convergence theorem and Arzelá-Ascoli xed point theorem on existence a...
Article
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The current analysis employs the improved F-expansion, modified extended tanh, exponential rational function, and (g′)−expansion procedures to find a divergent collection of the fractional Liouville equation’s exact solutions in the context of beta-derivative. Also, we have given the graphical representations of the obtained results. These plots ar...
Poster
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We are now serving as editors for the Special Issue "The 2022 3rd International Conference on Materials, Physics and Computers (MPC 2022)" at Symmetry, MDPI (https://www.mdpi.com/journal/symmetry/special_issues/The_2022_3rd_International_Conference_Materials_Physics_Computers_MPC_2022). I am calling for papers submission to our conference special i...
Article
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In this manuscript, Optimal Homotopy Asymptotic Method (OHAM) is used to find the approximate solutions of time fractional Phi-4 nonlinear partial differential equations. Approximate first order results are acquired through OHAM and are compared with the exact solutions. It has been noticed that the obtained results from OHAM have large convergence...
Poster
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I have been awarded the 2022 Peer Reviewer Extraordinaire Award from California State University, Long Beach, CA, USA for Major Contribution for the Mathematics Peer Review Process at the Multimedia Educational Resources for Learning and Online Teaching (MERLOT II) Program
Article
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A novel technique, named auxiliary equation method, is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems: the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional derivative. Our solutions were obtained using MAPLE software. This technique show...
Poster
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Reviewer Certificate on March 14, 2022 from the IET Communications (Q3 Journal) (Indexed by Scopus and Web of Science-SCIE) issued by Wiley
Article
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The COVID-19 pandemic has caused emotional loss to people around the world and provides an unusual test for public welfare, educational framework, food frameworks, and the world of work. The economic and social turmoil caused by this epidemic is increasing, and many people are at risk of falling into oppressive poverty. In this article, we describe...
Article
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In this work, a proposed system of fractional boundary value problems is investigated concerning its unbounded solutions' existence for a class of nonlinear fractional q-difference equations in the context of the Riemann-Liouville fractional q-derivative on an infinite interval. The system's solution is formulated with the help of Green's function....
Article
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Novel results on conformable Bessel functions are proposed in this study. We complete this study by proposing and proving certain properties of the Bessel functions of first order involving their conformable derivatives or their zeros. We also establish the orthogonality of such functions in the interval [0,1]. This study is essential due to the im...
Poster
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We are now serving as editors for the Special Issue "Applied Mathematics Fractional Calculus II " at Symmetry, MDPI (Indexed by Scopus and SCIE (Web of Science) with an impact factor of 2.713. This is the link for submission: (https://www.mdpi.com/journal/symmetry/special_issues/Applied_Mathematics_Fractional_Calculus_II). I am calling for papers s...
Article
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Human mortality is unanticipated and unavoidable, particularly in light of the recent COVID-19 pandemic. Insurance companies, actuaries, financial institutions, demographers, and the government may suffer catastrophic losses as a result of imprecise mortality estimates. Understanding the factors that contribute to mortality at the population level...
Poster
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We are now serving as editors for the Special Issue "The 2022 7th International Conference on Intelligent Information Processing" at Signals, MDPI (https://www.mdpi.com/journal/signals/special_issues/The_2022_7th_International_Conference_Intelligent_Information_Processing). This conference is hosted by the Romanian-American University in Bucharest,...
Article
Full-text available
In the research work, we discuss a multi-singular pointwise defined fractional q-integro-differential equation under some boundary conditions via the Riemann-Liouville q-integral and Caputo fractional q-derivatives. New existence results rely on the α-admissible map and fixed point theorem for α-ψ-contraction map. At the end, we present an example...
Poster
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I am serving as an editor for the 2022 3rd International Conference on Materials, Physics and Computers (MPC 2022) (http://ieti.net/m/index.html). All accepted papers will be published as conference proceedings in Institute of Physics (IOP): Journal of Physics Conference Series (indexed by Scopus, Ei Compendex, and Inspec(IET)). I am calling for pa...
Article
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Let G = (V, E) be a connected graph with diameter d and order n. A non-empty subset X of V is called a resolving set if for each pair u, v ∈ V such that u ̸ = v, then there is a vertex x in X satisfies d(x, u) ̸ = d(x, v). The minimum cardinality of all such resolving sets is called the resolving number of G. Let X be a non-empty minimum cardinalit...
Article
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The distance two labelling and radio labelling problems are applicable to find the optimal frequency assignments on AM and FM radio stations. The distance two labelling, known as L(2,1)-labelling of a graph A, can be defined as a function, , from the vertex set V(A) to the set of all non-negative integers such that represents the distance between t...
Article
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We find quantum systems having finite distinct discrete energy levels can reflect infinite distinct energy levels under suitable form of position dependent mass systems. A model example has been investigated considering the fractional Harmonic Oscillator [6].In addition to this,we also notice the same behaviour in other quantum models. In all the c...
Article
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Communication systems including AM and FM radio stations transmitting signals are capable of generating interference due to unwanted radio frequency signals. To avoid such interferences and maximize the number of channels for a predefined spectrum bandwidth, the radio-k-chromatic number problem is introduced. Let be a connected graph with diameter...
Article
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The Lorenz-Stenflo mathematical model describes a complex dynamical behavior related to atmospheric acoustic-gravity waves. In this study, qualitative analysis of the four-dimensional hyperchaotic Lorenz-Stenflo system via the Caputo fractional derivative is implemented. By using the Matignon stability criterion, the local stability analysis of the...
Article
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The main idea of this article is the investigation of atmospheric internal waves, often known as gravity waves. This arises within the ocean rather than at the interface. A shallow fluid assumption is illustrated by a series of nonlinear partial differential equations in the framework. Because the waves are scattered over a wide geographical region...
Poster
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I am now serving as "Review Editor" for the "Dynamical Systems" Section of Frontiers in Applied Mathematics and Statistics, indexed by SCOPUS and ESCI, published by Frontiers, which is owned by Nature Research, in Lausanne, Switzerland. I am calling for paper submissions to our section on this link: https://www.frontiersin.org/journals/applied-math...
Article
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Wireless communication systems have evolved and offered more smart and advanced systems like ad hoc and sensor-based infrastructure fewer networks. These networks are evaluated with two fundamental parameters including data rate and spectral efficiency. To achieve a high data rate and robust wireless communication, the most significant task is chan...
Poster
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My Certificate of Appreciation from the Faculty of Computer Science, University of Jember, Indonesia for my Service as a Reviewer for 2021 International Conference on Computer Science, Information Technology and Electrical Engineering (ICOMITEE) that was held in Banyuwangi, Indonesia on 27th-28th of October, 2021.
Preprint
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This paper revisits the topic of Pythagorean triples with a different perspective. While numerous methods were explored to generate Pythagorean triples, none of them is whole in terms of producing all of the triples without repetitions. Indeed, many current methods focus on producing primitive triples but there does not exist multiple triples.We ex...
Article
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Review of “Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images” by Carolina A. Mosquera and Pablo S. Shmerkin is submitted to Zentralblatt MATH (zbMATH), FIZ Karlsruhe, Berlin, Germany; Zbl 06964597.
Article
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Review of “High-order multi-material ALE hydrodynamics” by Robert W. Anderson, Veselin A. Dobrev, Tzanio V. Kolev, Robert N. Rieben, and Vladimir Z. Tomov is submitted to Zentralblatt MATH (zbMATH), FIZ Karlsruhe, Berlin, Germany; Zbl 06828359.
Article
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Review of “New Monte Carlo algorithms for estimating probability moments of criticality parameters for a scattering process with multiplication in stochastic media” by G. A. Mikhailov and G. Z. Lotova is submitted to Zentralblatt MATH (zbMATH), FIZ Karlsruhe, Berlin, Germany; Zbl 06892211.
Article
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Review of “Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation” by Hailiang Liu and Peimeng Yin is submitted to Zentralblatt MATH (zbMATH), FIZ Karlsruhe, Berlin, Germany; Zbl 07309642.
Conference Paper
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With the rapid development of Internet education, according to the trend of educational technology integration under the new situation, the Ministry of Education proposes that making full use of modern educational resources and advanced technology, building a mobile learning environment, and making efficient use of 5G network environment for mobile...
Conference Paper
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Depth’ is taken to be the ‘cable depth’ by logging system that is collected at regular depth intervals. Due to the distortion of log measurement caused by cable stretch, irregular motion, and imaging logging tool sticking, serious distortion of logging image occurs, which affects the preparation and acquisition of geological information. Therefore,...
Article
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In this work, the Catalan transformation (CT) of k-balancing sequences, 􏽮Bk,n􏽯n≥0, is introduced. Furthermore, the obtained Catalan transformation CB􏽮 k,n􏽯n≥0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k-balancing sequences, B􏽮 k,n􏽯n≥0, which is an n × 1 matrix. Apart from that, the Hankel transf...
Article
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In this article, the approximate analytical solutions of four different types of conformable partial differential equations are investigated. First, the conformable Laplace transform homotopy perturbation method is reformulated. Then, the approximate analytical solution of four types of conformable partial differential equations is presented via th...
Article
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The current work aims to present abundant families of the exact solutions of Mikhailov-Novikov-Wang equation via three different techniques. The adopted methods are generalized Kudryashov method (GKM), exponential rational function method (ERFM), and modified extended tanh-function method (METFM). Some plots of some presented new solutions are repr...
Article
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Developing new treatments for emerging infectious diseases in infectious and noninfectious diseases has attracted a particular attention. The emergence of viral diseases is expected to accelerate; these data indicate the need for a proactive approach to develop widely active family specific and cross family therapies for future disease outbreaks. V...
Conference Paper
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With the rapid development of smart terminals, as well as the diverse applications of demand, existing networks may not be able to meet the fast-growing traffic demands in academia as Tencent meeting, zoom TV and other online education resources etc. Therefore, researchers have focused on Future Robust Network (FRC) communication to achieve a suffi...
Article
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Wireless sensor networks (WSNs) are subject to cyber attacks. Security of such networks is a significant priority for everyone. Due to the network's frail defense mechanisms, WSNs are easy targets for worm attacks. A single unsecured node via contact can effectively propagate the worm across the entire network. Mathematical epidemic models are help...
Article
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The Black-Scholes model is well known for determining the behavior of capital asset pricing models in the finance sector. The present article deals with the Black-Scholes model via the Caputo fractional derivative and Atangana-Baleanu fractional derivative operator in the Caputo sense, respectively. The Jafari transform is merged with the Adomian d...
Poster
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I am very happy that I have been invited as a keynote speaker to give a talk at the II International Scientific and Practical Conference "Ecology. Environment. Energy saving » held in Yuri Kondratyuk Poltava Polytechnic National University, Poltava, Ukraine. It was a great honor to share my most updated research contributions.
Article
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Alzheimer’s disease (AD) is a leading health concern affecting the elderly population worldwide. It is defined by amyloid plaques, neurofibrillary tangles, and neuronal loss. Neuroimaging modalities such as positron emission tomography (PET) and magnetic resonance imaging are routinely used in clinical settings to monitor the alterations in the bra...
Article
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An interesting quadratic fractional integral equation is investigated in this work via a generalized Mittag-Leffler (ML) function. The generalized ML–Hyers–Ulam stability is established in this investigation. We study both of the Hyers–Ulam stability (HUS) and ML–Hyers–Ulam–Rassias stability (ML-HURS) in detail for our proposed differential equatio...
Article
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New investigation on the conformable version (CoV) of multivariable calculus is proposed. The conformable derivative (CoD) of a real-valued function (RVF) of several variables (SVs) and all related properties are investigated. An extension to vector-valued functions (VVFs) of several real variables (SRVs) is studied in this work. The CoV of chain r...
Preprint
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This preprint is submitted to Zentralblatt MATH (zbMATH), FIZ Karlsruhe, Berlin, Germany; Zbl 07286084.
Article
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In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic so...
Article
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This study intends to examine different dynamics of the chaotic incommensurate fractional-order Hopfield neural network model. The stability of the proposed incommensurate-order model is analyzed numerically by continuously varying the values of the fractional-order derivative and the values of the system parameters. It turned out that the formulat...
Article
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Deep learning (DL) is a branch of machine learning and artificial intelligence that has been applied to many areas in different domains such as health care and drug design. Cancer prognosis estimates the ultimate fate of a cancer subject and provides survival estimation of the subjects. An accurate and timely diagnostic and prognostic decision will...
Article
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The Rath's mannequin approximation is generalized in this work to generate finite strength level(s) quantum structures in Hermitian and non-Hermitian quantum systems. On one hand, in Hermitian systems, an extensive variety of bounded single properly,triple nicely, and pentic proper systems is utilized. On the other hand, isospectral Hermitian struc...