Prof. Dr. Hadid is a Faculty member in the Department of Mathematics and Sciences at Ajman University since 1999. He obtained his PhD degree from London University in 1979, and became a professor in Mathematics since 1995. Prof. Dr. Hadid is author of 4 books in Mathematics, and has published more than 90 papers, and about 250 articles in heritage and culture. In addition, Prof. Dr. Hadid is the author of the book “Mosul Heritage" and another book on Mosul in print. Has held several administrative academic positions such as, Head of Department and Dean at Ajman University and other universities, and vice chancellor at Al Ain University. He participated in more than 40 national and international conferences, and was an invited speaker in three of them. Prof. Dr. Hadid has an excellent teaching record. He taught Mathematics for Engineering and Sciences for more than 40 years. Recently, he is involved in the most widespread definitions of the concepts of Mission, Goals, Objectives and Outcomes of an educational program. He has been using mathematical software in teaching Mathematics. In particular, He uses Mathematica and Mat-lab in teaching Calculus, Differential Equations, and Engineering Mathematics. Since 2010, He initiated a research group from 5 international universities, with a main research interest in Fractional Differential Equations and Applications.”
The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results
The pivotal aim of this paper is to investigate analytical and numerical solutions of fractional fuzzy hybrid system in Hilbert space. Such fuzzy systems are devoted to model control systems that are capable of controlling complex systems that have discrete events with continuous time dynamics. The fractional derivative is described in Atangana-Baleanu Caputo (ABC) sense, which is distinguished by its non-local and non-singular kernel. In this orientation, the main contribution of the current numerical investigation is to generalize the characterization theory of integer fuzzy IVP to the ABC-fractional derivative under a strongly generalized differentiability, and then apply the proposed method to deal with the fuzzy hybrid system numerically. This method optimized the approximate solutions based on orthogonalization Schmidt process on Sobolev spaces, which can be straightway employed in generating Fourier expansion within a sensible convergence rate. The reproducing kernel theory is employed to construct a series solution with parametric form for the considered model in the space of direct sum W2 2 [a, b] ⊕ W2 2 [a, b]. Some theorems related to convergence analysis and approximation error are also proved. Moreover, we obtain the exact solution for the fuzzy model by applying Laplace transform method. So, the results obtained using the proposed method are compared with those of exact solution. To show the effect of AtanganaBaleanu fractional operator, we compare the numerical solution of fractional fuzzy hybrid system with those of integer order. Two numerical examples are carried out to illustrate that such dynamical processes noticeably depend on time instant and time history, which can be efficiently modeled by employing the fractional calculus theory. Finally, the accuracy, efficiency, and simplicity of the proposed method are evident in both classical and fractional cases
Nowadays, the complete world is suffering from untreated infectious epidemic disease COVID-19 due to coronavirus, which is a very dangerous and deadly viral infection. So, the major desire of this task is to propose some new mathematical models for the coronavirus pandemic (COVID-19) outbreak through fractional derivatives. The adoption of modified mathematical techniques and some basic explanation in this research field will have a strong effect on progressive society fitness by controlling some diseases. The main objective of this work is to investigate the dynamics and numerical approximations for the recommended arbitrary-order coronavirus disease system. This system illustrating the probability of spread within a given general population. In this work, we considered a system of a novel COVID-19 with the three various arbitrary-order derivative operators: Caputo derivative having the power law, Caputo–Fabrizio derivative having exponential decay law and Atangana–Baleanu-derivative with generalized Mittag–Leffler function. The existence and uniqueness of the arbitrary-order system is investigated through fixed-point theory. We investigate the numerical solutions of the non-linear arbitrary-order COVID-19 system with three various numerical techniques. For study, the impact of arbitrary-order on the behavior of dynamics the numerical simulation is presented for distinct values of the arbitrary power ????.
We present a fractional series solution (FSS) for a class of higher-order linear fractional PDEs. The fractional derivative in this class is considered in the conformable fractional derivative (Co-FD) sense. An appropriate expansion was introduced to reach an FSS that is consistent with the target equations in this research. The residual power series technique is used to determine the coefficients of the FSS. Five applications are tested to verify the effectiveness of the used method, as well as to compare the current results with the previous results for the same applications in which the fractional derivative was considered in the Caputo sense. Numerical and graphical comparisons are made to determine the compatibility of the behavior of the solution in the case of the use of the concept of Co-FD as a suitable alternative to the use of the concept of Caputo fractional derivative (Ca-FD) in the modeling of natural phenomena
Abstract: The economic order quantity (EOQ) design indicates the cost that reduces the assembly collective of charge payment functions. One of the accept dynamic simulations is that given by the concept of entropy, which is a so-called entropy order quantity (EnOQ). It introduces a potential progress to grow construction organizations developing by applying the theory of information. In this work, we present a dynamic system for EOQ, by utilizing a special type of fractional calculus named conformable calculus. We present the generalized conformable entropy order quantity (C-EnOQ). In this situation, we supply the cost functions with reference to time in a recurring dated. In this system, we consider the linked optimization issue and improve an uninterrupted method for figuring a bounded interval casing the optimal arrangement expanse, exploiting the Tsallis fractional entropy. Moreover, for an astonishing class of transference functions, we explore these cost functions to compute the optimal magnitude.
Investigators display that there is a central connotation between traveling wave results and the symmetric. They have exposed that all traveling waves are symmetric waves. In this investigation, we present holomorphic assemblies of a class of nonlinear conformable time-fractional wave equations type Khokhlov-Zabolotskaya (KZ) in a complex purview. For this aim, we introduce a characterization of a complex conformable calculus (CCC) of a symmetric differential operator (SDO) and study its properties. Moreover, the operator is extended to a complex domain satisfying symmetric illustrations. By employing the proposed operator, we generalize KZ equation symmetrically. The indications imply that the suggested techniques are powerful, reliable and express to employ all styles of differential equations of complex variables.
The population model has an important role in biology to interpret the spreading rate of viruses and parasites. This biological model is also used to identify fragile species. This paper aims to propose a new Yang-Abdel-Aty-Cattani (YAC) fractional operator with a non-singular kernel to solve nonlinear partial differential equation, which is arised in biological population model. Here, this study has explained the analytical methods, reduced differential transform method (RDTM) and residual power series method (RPSM) taking the fractional derivative as YAC operator sense.
There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus. We investigate a fractional system of integro-differential equations, which covers the subtleties of the diffusion between infected and asymptomatic cases. The suggested system is applicable to distinguish the presentation of growth level of the infection and to approve if its mechanism is positively active. An optimal solution under simulation mapping assets is considered. The estimated numerical solution is indicated by employing the fractional Tutte polynomials. Our methodology is based on the Atangana–Baleanu calculus (ABC). We assess the recommended system by utilizing real data.
There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus. We investigate a fractional system of integro-differential equations, which covers the subtleties of the diffusion between infected and asymptomatic cases. The suggested system is applicable to distinguish the presentation of growth level of the infection and to approve if its mechanism is positively active. An optimal solution under simulation mapping assets is considered. The estimated numerical solution is indicated by employing the fractional Tutte polynomials. Our methodology is based on the Atangana–Baleanu calculus (ABC). We assess the recommended system by utilizing real data.
The main purpose of the proposed work is to study a TB infection model under incomplete treatment numerically and identify potential infection dynamics. We use the arbitrary-order Caputo-Fabrizio (CF) and AtanganaBaleanu (AB) derivatives to extend the classical TB infection model into a non-classical model. In addition, through fixed-point results, the existence and uniqueness of solutions for the arbitrary order TB model are discussed. We illustrate computational techniques from existing literature for the numerical solutions of the mentioned fractional models. The numerical simulations are presented using MATLAB software with various choices of the fractional-order parameter
Newly, numerous investigations are considered utilizing the idea of parametric operators (integral and differential). The objective of this effort is to formulate a new 2D-parametr differential operator (PDO) of a class of multivalent functions in the open unit disk. Consequently, we formulate the suggested operator in some interesting classes of analytic functions to study its geometric properties. The recognized class contains some recent works. Keywords: univalent function; analytic function; open unit disk; Subordination and super ordination; fractional calculus; parametric differential operator.
A conformable fractional time derivative of order α ∈ (0, 1] is considered instead of the classical time derivative α = 1 in the Lax-pair operator which leads to a fractional nonlinear evolution system of Four-Wave-Interaction-Equations 4-WIE’s. The resulted system is then solved by an ansatz contains tan and secant hyperbolic functions with complex coefficients.A systematic steps are introduced to obtain a general form of exact soliton solutions for the resulted system in (1+1) one spatial and one temporal dimensions. We showed that the obtained solutions could be modified to represent solutions of a similar system but in (2+1) two spatial and one temporal dimensions too. In fact, our suggested ansatz can be used to obtain exact soliton solutions for fractional N-Wave-Interaction-Equations N-WIE’s in one or more spatial dimensions for N greater than or equal to four. Then we state some numerical examples with their 3-D graphs, these examples of solutions give a better understanding to the behavior of the soliton waves while the interaction turned on
Abstract The current study’s aim is to evaluate the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers using two different numerical algorithms and various values of the fractionalorder parameter. We considered the model with two different fractional-order derivatives, namely the Caputo derivative and Atangana–Baleanu derivative in the Caputo sense (ABC). The considered derivatives are the most widely used fractional operators in modeling. We present some mathematical analysis of the fractional ABC model. The fixed-point theory is used to determine the existence and uniqueness of the solutions to the considered fractional model. For numerical results, we show a generalized Adams– Bashforth–Moulton (ABM) method for Caputo derivative and an Adams type predictor-corrector (PC) algorithm for Atangana–Baleanu derivatives. Finally, the models are numerically solved using computational techniques and obtained results graphically illustrated with a wide range of fractional-order values. We compare the numerical results for Caputo and ABC derivatives graphically. In addition, a new variable-order fractional network of the HBV model is proposed. Considering the fact that most communities interact with each other, and the rate of disease spread is affected by this factor, the proposed network can provide more accurate insight for the modeling of the disease.
In a complex domain, the investigation of the quantum differential subordinations for starlike functions is newly considered by few researches. In this note, we arrange a set of necessary conditions utilizing the concept of the quantum differential subordinations for starlike functions related to the set of parametric Julia functions. Our method is based on the usage of quantum Jack lemma, where this lemma is generalized recently by the quantum derivative (Jackson calculus). We illustrate a starlike formula dominated by different types of Julia functions. The sufficient conditions are computed in the quantum and the Julia fractional parameters. We indicate a relationship between these two parameters.
Electrical engineering models can typically be simulated with a circuit of interconnected electrical components containing electrically charged particles that can be moved from atom to atom across a closed conducting pathway. In this paper, the electric circuit model of fractional stiff differential equations is investigated using a novel multi-step approach of reproducing kernel method (MS-RKM). Fractional operator with non-singular kernel, Caputo-Fabrizio fractional derivative, is considered to obtain accurate approximate solutions over a sequence of intervals for the fractional stiff system. To maintain dimensionality of the physical parameters appearing in the electrical circuit, a parameter is used to characterize the presence of fractional structures in the electrical model. Solving our model, in the context of classic numerical methods, is a difficult task, and solutions are often offered in a very small region with a very slow rate of convergence or they may diverge in wider regions. MS-RKM is treated as a new modification of RKM on subintervals, which considerably reduces the number of arithmetic operations and thus time and effort to get approximate solutions. Efficiency, simplicity, and accuracy of the proposed multi-step approach in solving the fractional stiff system is evident through numerical simulations performed for RL, RC, and RLC circuit models.
We used the concept of quantum calculus (Jackson’s calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class. The most common inequalities of the proposed functions are geometrically investigated. Our approach was influenced by the theory of differential subordination. As a result, we called attention to a few well-known corollaries of our main conclusions.