Browsing by Author "Al Qurashi, Maysaa"

Now showing 1 - 18 of 18

Citation - WoS: 30
Citation - Scopus: 33
Analysis of a New Fractional Model for Damped Bergers' Equation
(de Gruyter Open Ltd, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we present a fractional model of the damped Bergers' equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.
Citation - WoS: 46
Citation - Scopus: 49
Analysis of Logistic Equation Pertaining To a New Fractional Derivative With Non-Singular Kernel
(Sage Publications Ltd, 2017) Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, Devendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo-Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.
Citation - WoS: 25
Citation - Scopus: 47
Approximate Analytical Solutions of Goursat Problem Within Local Fractional Operators
(int Scientific Research Publications, 2016) Jassim, Hassan Kamil; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The local fractional differential transform method (LFDTM) and local fractional decomposition method (LFDM) are applied to implement the homogeneous and nonhomogeneous Goursat problem involving local fractional derivative operators. The approximate analytical solution of this problem is calculated in form of a series with easily computable components. Examples are studied in order to show the accuracy and reliability of presented methods. We demonstrate that the two approaches are very effective and convenient for finding the analytical solutions of partial differential equations with local fractional derivative operators. (C) 2016 All rights reserved.
Citation - WoS: 12
Citation - Scopus: 11
A Computational Study of a Stochastic Fractal-Fractional Hepatitis B Virus Infection Incorporating Delayed Immune Reactions Via the Exponential Decay
(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Al Qurashi, Maysaa; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order delta with constant fractal-dimension pi, delta with changing pi, and delta with changing both delta and pi. White noise concentration has a significant impact on how bacterial infections are treated.
Citation - WoS: 41
Citation - Scopus: 46
An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems
(Mdpi, 2020) Khan, Adnan; Ali, Izaz; Al Qurashi, Maysaa; Khan, Hassan; Shah, Rasool; Baleanu, Dumitru; Qin, Ya; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Mostly, it is very difficult to obtained the exact solution of fractional-order partial differential equations. However, semi-analytical or numerical methods are considered to be an alternative to handle the solutions of such complicated problems. To extend this idea, we used semi-analytical procedures which are mixtures of Laplace transform, Shehu transform and Homotopy perturbation techniques to solve certain systems with Caputo derivative differential equations. The effectiveness of the present technique is justified by taking some examples. The graphical representation of the obtained results have confirmed the significant association between the actual and derived solutions. It is also shown that the suggested method provides a higher rate of convergence with a very small number of calculations. The problems with derivatives of fractional-order are also solved by using the present method. The convergence behavior of the fractional-order solutions to an integer-order solution is observed. The convergence phenomena described a very broad concept of the physical problems. Due to simple and useful implementation, the current methods can be used to solve problems containing the derivative of a fractional-order.
Citation - WoS: 88
The Extended Mittag-Leffler Function Via Fractional Calculus
(int Scientific Research Publications, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa; Purohit, Sunil Dutt; Mubeen, Shahid; Arshad, Muhammad; Rahman, Gauhar; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this study, our main attempt is to introduce fractional calculus (fractional integral and differential) operators which contain the following new family of extended Mittag-Leffler function: E-alpha,beta(gamma;q,c) (z) = Sigma(infinity)(n=0) B-p (gamma + nq, c - gamma)(c)(nq) z(n)/B(gamma, c - gamma)Gamma(alpha n + beta) n!' (z,beta,gamma is an element of C), as its kernel. We also investigate a certain number of their consequences containing the said function in their kernels. (C) 2017 All rights reserved.
Citation - WoS: 8
Citation - Scopus: 10
Fractional-Order Partial Differential Equations Describing Propagation of Shallow Water Waves Depending on Power and Mittag-Leffier Memory
(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Sultana, Sobia; Jarad, Fahd; Alsharif, Abdullah M.; Al Qurashi, Maysaa; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this research, the (q) over bar -homotopy analysis transform method ((q) over bar -HATM) is employed to identify fractional-order Whitham-Broer-Kaup equation (WBKE) solutions. The WBKE is extensively employed to examine tsunami waves. With the aid of Caputo and Atangana-Baleanu fractional derivative operators, to obtain the analytical findings of WBKE, the predicted algorithm employs a combination of (q) over bar -HAM and the Aboodh transform. The fractional operators are applied in this work to show how important they are in generalizing the frameworks connected with kernels of singularity and non-singularity. To demonstrate the applicability of the suggested methodology, various relevant problems are solved. Graphical and tabular results are used to display and assess the findings of the suggested approach. In addition, the findings of our recommended approach were analyzed in relation to existing methods. The projected approach has fewer processing requirements and a better accuracy rate. Ultimately, the obtained results reveal that the improved strategy is both trustworthy and meticulous when it comes to assessing the influence of nonlinear systems of both integer and fractional order.
Citation - WoS: 84
A Modified Analytical Approach With Existence and Uniqueness for Fractional Cauchy Reaction-Diffusion Equations
(Springer, 2020) Kumar, Amit; Abbas, Syed; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, Sunil; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction-diffusion equations (TFCRDEs). Then mainly we address the error norms L2 and L infinity for a convergence study of the proposed method. We also find existence, uniqueness and convergence in the analysis for TFCRDEs. The projected method is illustrated by solving some numerical examples. The obtained numerical solutions by the HATM method show that it is simple to employ. An excellent conformity obtained between the solution got by the HATM method and the various well-known results available in the current literature. Also the existence and uniqueness of the solution have been demonstrated.
Citation - WoS: 67
Citation - Scopus: 79
New Exact Solutions of the Generalized Benjamin-Bona Equation
(Mdpi, 2019) Baleanu, Dumitru; Al Qurashi, Maysaa; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The recently introduced technique, namely the generalized exponential rational function method, is applied to acquire some new exact optical solitons for the generalized Benjamin-Bona-Mahony (GBBM) equation. Appropriately, we obtain many families of solutions for the considered equation. To better understand of the physical features of solutions, some physical interpretations of solutions are also included. We examined the symmetries of obtained solitary waves solutions through figures. It is concluded that our approach is very efficient and powerful for integrating different nonlinear pdes. All symbolic computations are performed in Maple package.
Citation - WoS: 138
Citation - Scopus: 157
A New Fractional Model for Giving Up Smoking Dynamics
(Springeropen, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The key purpose of the present work is to examine a fractional giving up smoking model pertaining to a new fractional derivative with non-singular kernel. The numerical simulations are conducted with the aid of an iterative technique. The existence of the solution is discussed by employing the fixed point postulate, and the uniqueness of the solution is also proved. The effect of various parameters is shown graphically. The numerical results for the smoking model associated with the new fractional derivative are compared with numerical results for a smoking model pertaining to the standard derivative and Caputo fractional derivative.
Citation - WoS: 155
Citation - Scopus: 147
A New Fractional Sirs-Si Malaria Disease Model With Application of Vaccines, Antimalarial Drugs, and Spraying
(Springer, 2019) Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, Devendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo-Fabrizio fractional operator for the inclusion of memory. We also suggest the utilization of vaccines, antimalarial medicines, and spraying for the treatment and control of the malaria disease. The theory of fixed point is utilized to examine the existence of the solution of a fractional SIRS-SI model describing spreading of malaria. The uniqueness of the solution of SIRS-SI model for malaria is also analyzed. It is shown that the treatments have great impact on the dynamical system of human and mosquito populations. The numerical simulation of fractional SIRS-SI malaria model is performed with the aid of HATM and Maple packages to show the effect of different parameters of the treatment of malaria disease. The numerical results for fractional SIRS-SI malaria model reveal that the recommended approach is very accurate and effective.
Citation - WoS: 17
Citation - Scopus: 18
New Numerical Dynamics of the Fractional Monkeypox Virus Model Transmission Pertaining To Nonsingular Kernels
(Amer inst Mathematical Sciences-aims, 2023) Rashid, Saima; Alshehri, Ahmed M.; Jarad, Fahd; Safdar, Farhat; Al Qurashi, Maysaa; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Monkeypox (MPX) is a zoonotic illness that is analogous to smallpox. Monkeypox infections have moved across the forests of Central Africa, where they were first discovered, to other parts of the world. It is transmitted by the monkeypox virus, which is a member of the Poxviridae species and belongs to the Orthopoxvirus genus. In this article, the monkeypox virus is investigated using a deterministic mathematical framework within the Atangana-Baleanu fractional derivative that depends on the generalized Mittag-Leffler (GML) kernel. The system's equilibrium conditions are investigated and examined for robustness. The global stability of the endemic equilibrium is addressed using Jacobian matrix techniques and the Routh-Hurwitz threshold. Furthermore, we also identify a criterion wherein the system's disease-free equilibrium is globally asymptotically stable. Also, we employ a new approach by combining the two-step Lagrange polynomial and the fundamental concept of fractional calculus. The numerical simulations for multiple fractional orders reveal that as the fractional order reduces from 1, the virus's transmission declines. The analysis results show that the proposed strategy is successful at reducing the number of occurrences in multiple groups. It is evident that the findings suggest that isolating affected people from the general community can assist in limiting the transmission of pathogens.
Citation - WoS: 44
Citation - Scopus: 49
A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships
(Mdpi, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian's decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter h and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
Citation - WoS: 14
Citation - Scopus: 32
On the Existence and Uniqueness of Solutions for Local Fractional Differential Equations
(Mdpi, 2016) Baleanu, Dumitru; Jafari, Hossein; Jassim, Hassan Kamil; Al Qurashi, Maysaa; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasing theorem (IDT), existence and uniqueness results are obtained. Some examples are presented to illustrate the validity of our results.
Citation - WoS: 4
Citation - Scopus: 8
Retracted: an Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique (Retracted Article)
(Wiley-hindawi, 2020) Khan, Adnan; Al Qurashi, Maysaa; Baleanu, Dumitru; Shah, Rasool; Khan, Hassan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, a new so-called iterative Laplace transform method is implemented to investigate the solution of certain important population models of noninteger order. The iterative procedure is combined effectively with Laplace transformation to develop the suggested methodology. The Caputo operator is applied to express the noninteger derivative of fractional order. The series form solution is obtained having components of convergent behavior toward the exact solution. For justification and verification of the present method, some illustrative examples are discussed. The closed contact is observed between the obtained and exact solutions. Moreover, the suggested method has a small volume of calculations; therefore, it can be applied to handle the solutions of various problems with fractional-order derivatives.
Citation - WoS: 27
Citation - Scopus: 27
Solitons and Jacobi Elliptic Function Solutions To the Complex Ginzburg-Landau Equation
(Frontiers Media Sa, 2020) Hosseini, Kamyar; Mirzazadeh, Mohammad; Osman, M. S.; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The complex Ginzburg-Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified Jacobi elliptic expansion method. In special cases, several dark and bright soliton solutions to the CGL equation are retrieved when the modulus of ellipticity approaches unity. The results presented in the current work can help to complete previous studies on the complex Ginzburg-Landau equation.
Citation - WoS: 32
Citation - Scopus: 58
Solving Helmholtz Equation With Local Fractional Derivative Operators
(Mdpi, 2019) Jassim, Hassan Kamil; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The paper presents a new analytical method called the local fractional Laplace variational iteration method (LFLVIM), which is a combination of the local fractional Laplace transform (LFLT) and the local fractional variational iteration method (LFVIM), for solving the two-dimensional Helmholtz and coupled Helmholtz equations with local fractional derivative operators (LFDOs). The operators are taken in the local fractional sense. Two test problems are presented to demonstrate the efficiency and the accuracy of the proposed method. The approximate solutions obtained are compared with the results obtained by the local fractional Laplace decomposition method (LFLDM). The results reveal that the LFLVIM is very effective and convenient to solve linear and nonlinear PDEs.
Citation - WoS: 13
Citation - Scopus: 28
Some Fractional Calculus Findings Associated With the Incomplete I-Functions
(Springer, 2020) Bhatter, Sanjay; Meena, Sapna; Baleanu, Dumitru; Al Qurashi, Maysaa; Purohit, Sunil Dutt; Jangid, Kamlesh; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, several interesting properties of the incomplete I-functions associated with the Marichev-Saigo-Maeda (MSM) fractional operators are studied and investigated. It is presented that the order of the incomplete I-functions increases about the utilization of the above-mentioned operators toward the power multiple of the incomplete I-functions. Further, the Caputo-type MSM fractional order differentiation for the incomplete I-functions is studied and investigated. Saigo, Riemann-Liouville, and Erdelyi-Kober fractional operators are also discussed as specific cases.