Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 6Citation - Scopus: 6Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage(Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, ThabetMiddle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.Article Citation - WoS: 51Citation - Scopus: 66Existence and Uniqueness of Solutions to Fractional Differential Equations in the Frame of Generalized Caputo Fractional Derivatives(Springer, 2018) Gambo, Y. Y.; Ameen, R.; Jarad, Fahd; Abdeljawad, T.The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607-2619, 2017). Depending on the value of. in the limiting case, the generality of the derivative is that it gives birth to two different fractional derivatives. However, the existence and uniqueness of solutions to fractional differential equations with generalized Caputo fractional derivatives have not been proven. In this paper, Cauchy problems for differential equations with the above derivative in the space of continuously differentiable functions are studied. Nonlinear Volterra type integral equations of the second kind corresponding to the Cauchy problem are presented. Using Banach fixed point theorem, the existence and uniqueness of solution to the considered Cauchy problem is proven based on the results obtained.Article Citation - WoS: 11Citation - Scopus: 12Some Symmetric Properties and Applications of Weighted Fractional Integral Operator(World Scientific Publ Co Pte Ltd, 2023) Samraiz, Muhammad; Mehmood, Ahsan; Jarad, Fahd; Naheed, Saima; Wu, ShanheIn this paper, a weighted generalized fractional integral operator based on the Mittag-Leffler function is established, and it exhibits symmetric characteristics concerning classical operators. We demonstrate the semigroup property as well as the boundedness of the operator in absolute continuous like spaces. In this work, some applications with graphical representation are also considered. Finally, we modify the weighted generalized Laplace transform and then applied it to the newly defined weighted fractional integral operator. The defined operator is an extension and generalization of classical Riemann-Liouville and Prabhakar integral operators.Article Citation - WoS: 32Citation - Scopus: 33On the Multiparameterized Fractional Multiplicative Integral Inequalities(Springer, 2024) Saleh, Wedad; Lakhdari, Abdelghani; Jarad, Fahd; Meftah, Badreddine; Almatrafi, Mohammed BakheetWe introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus.Article Citation - WoS: 32Citation - Scopus: 31On Parameterized Inequalities for Fractional Multiplicative Integrals(de Gruyter Poland Sp Z O O, 2024) Meftah, Badreddine; Xu, Hongyan; Jarad, Fahd; Lakhdari, Abdelghani; Zhu, Wen ShengIn this article, we present a one-parameter fractional multiplicative integral identity and use it to derive a set of inequalities for multiplicatively s s -convex mappings. These inequalities include new discoveries and improvements upon some well-known results. Finally, we provide an illustrative example with graphical representations, along with some applications to special means of real numbers within the domain of multiplicative calculus.Article Citation - WoS: 2Citation - Scopus: 2Numerical Analysis for Hidden Chaotic Behavior of a Coupled Memristive Dynamical System Via Fractal-Fractional Operator Based on Newton Polynomial Interpolation(World Scientific Publ Co Pte Ltd, 2023) Ahmad, Shabir; Yassen, Mansour F.; Asiri, Saeed Ahmed; Ashraf, Abdelbacki M. M.; Saifullah, Sayed; Jarad, Fahd; Abdelmohsen, Shaimaa A. M.Dynamical features of a coupled memristive chaotic system have been studied using a fractal-fractional derivative in the sense of Atangana-Baleanu. Dissipation, Poincare section, phase portraits, and time-series behaviors are all examined. The dissipation property shows that the suggested system is dissipative as long as the parameter g > 0. Similarly, from the Poincare section it is observed that, lowering the value of the fractal dimension, an asymmetric attractor emerges in the system. In addition, fixed point notions are used to analyze the existence and uniqueness of the solution from a fractal-fractional perspective. Numerical analysis using the Adams-Bashforth method which is based on Newton's Polynomial Interpolation is performed. Furthermore, multiple projections of the system with different fractional orders and fractal dimensions are quantitatively demonstrated, revealing new characteristics in the proposed model. The coupled memristive system exhibits certain novel, strange attractors and behaviors that are not observable by the local operators.Article Citation - WoS: 10Citation - Scopus: 10Novel Investigation of Stochastic Fractional Differential Equations Measles Model Via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel(Tech Science Press, 2024) Jarad, Fahd; Rashid, SaimaBecause of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real -world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leff ler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions. Several numerical simulations for various fractional orders and randomization intensities are illustrated.Article Citation - WoS: 10Citation - Scopus: 11New Insights for the Fuzzy Fractional Partial Differential Equations Pertaining To Katugampola Generalized Hukuhara Differentiability in the Frame of Caputo Operator and Fixed Point Technique(Elsevier, 2024) Jarad, Fahd; Alamri, Hind; Rashid, SaimaIn this article, we use the Caputo-Katugampola gH-differentiability to solve a class of fractional PDE systems. With the aid of Caputo-Katugampola gH-differentiability, we demonstrate the existence and uniqueness outcomes of two types of gH-weak findings of the framework of fuzzy fractional coupled PDEs using Lipschitz assumptions and employing the Banach fixed point theorem with the mathematical induction technique. Moreover, owing to the entanglement in the initial value problems (IVPs), we establish the p Gronwall inequality of the matrix pattern and inventively explain the continuous dependence of the coupled framework's responses on the given assumptions and the epsilon-approximate solution of the coupled system. An illustrative example is provided to demonstrate that their existence and unique outcomes are accurate. Through experimentation, we demonstrate the efficacy of the suggested approach in resolving fractional differential equation algorithms under conditions of uncertainty found in engineering and physical phenomena. Additionally, comparisons are drawn for the computed outcomes. Ultimately, we make several suggestions for futuristic work.Article Citation - WoS: 35Citation - Scopus: 38Heat Transfer Analysis of Magnetized Cu-Ag Hybrid Nanofluid Radiative Flow Over a Spinning Disk When the Exponential Heat Source and Hall Current Are Substantial: Optimization and Sensitivity Analysis(Elsevier, 2023) Pyari, Devarsu Radha; Ontela, Surender; Al-Mdallal, Qasem M.; Jarad, Fahd; Thumma, ThirupathiThe main motive of the instigated mathematical model is to observe the impact of Hall current on the hybrid nanofluid flow over a disk that is rotating. The copper and silver metal nanoparticles have been considered with volume fraction phi 1 = phi 2 = 0.01(0.01)0.04 and are suspended in water to form the hybrid nanofluid. Diverse characteristics like magnetic field, thermal radiation, and (ESHS) exponential space dependent heat source are incorporated to investigate the nature of the flow. The present mathematical model is initiated with partial derivative equations (PDEs) which are redrafted as ordinary derivative equations (ODEs) with appropriate transformations of similarity. The results are attained through a blend of the Runge-Kutta method, shooting procedure, and the influences of parameters on the flow of nanofluid and hybrid nanofluid are compared and illustrated both as tables and graphs. The present numerical research is unique because by employing a complete quadratic CCD framework using the RSM strategy, the sensitivity and optimization analysis of the heat transmission improvement for the volume fraction, ESHS, and thermal radiation parameters have been performed. The R-squared and adjusted R-Squared are obtained as 100%. The residual graphs and contour diagrams of the same are also shown. The current study establishes that the Hall parameter increases the radial velocity, but it also controls the energy and cross-radial velocity. The rate of heat transmission is increased by thermal radiation even at low levels of ESHS. The rate of heat transmission is more sensitive (0.024670) to the volume fraction of the hybrid nanofluid when ESHS is at an intermediate level. The lowest sensitivity (-1.269967) value towards ESHS is observed For thermal radiation and ESHS parameter values, the heat transmission rate of the mono nanofluid is not as great as that of hybridArticle Citation - WoS: 6Citation - Scopus: 7Fixed Point Results in C*-Algebra Bipolar Metric Spaces With an Application(Amer inst Mathematical Sciences-aims, 2023) Gnanaprakasam, Arul Joseph; Isik, Huseyin; Jarad, Fahd; Mani, GunaseelanIn this work, we prove existence and uniqueness fixed point theorems under Banach and Kannan type contractions on C*-algebra-valued bipolar metric spaces. To strengthen our main results, an appropriate example and an effective application are presented.