Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article On the Finite Delayed Fractional Differential Equation via the Weighted Riemann-Liouville Derivative of Variable Order(World Scientific Publ Co Pte Ltd, 2026) Jarad, Fahd; Abdeljawad, Thabet; Souid, Mohammed Said; Hallouz, Abdelhamid; Alqudah, ManarThis study investigates the existence and uniqueness of solutions to initial value problems for nonlinear variable-order weighted fractional differential equations with finite delay. Building upon and generalizing prior constant-order fractional models, our approach employs fixed-point theory, specifically the Banach and Schauder fixed-point theorems, in suitable weighted function spaces to rigorously establish these fundamental results. We further demonstrate the applicability of our theoretical framework through illustrative examples. The findings contribute significantly to the mathematical understanding and modeling capabilities of complex systems exhibiting memory and hereditary properties governed by variable-order fractional dynamics.Article Citation - WoS: 9Citation - Scopus: 11Monkeypox Viral Transmission Dynamics and Fractional-Order Modeling With Vaccination Intervention(World Scientific Publ Co Pte Ltd, 2023) Kumar, Sachin; Baleanu, Dumitru; Nisar, Kottakkaran sooppy; Singh, Jaskirat palA current outbreak of the monkeypox viral infection, which started in Nigeria, has spread to other areas of the globe. This affects over 28 nations, including the United Kingdom and the United States. The monkeypox virus causes monkeypox (MPX), which is comparable to smallpox and cowpox (MPXV). The monkeypox virus is a member of the Poxviridae family and belongs to the Orthopoxvirus genus. In this work, a novel fractional model for Monkeypox based on the Caputo derivative is explored. For the model, two equilibria have been established: disease-free and endemic equilibrium. Using the next-generation matrix and Castillo's technique, if R-0 < 1 the global asymptotic stability of disease-free equilibrium is shown. The linearization demonstrated that the endemic equilibrium point is locally asymptotically stable if R-0 > 1. Using the parameter values, the model's fundamental reproduction rates for both humans and non-humans are calculated. The existence and uniqueness of the solution are proved using fixed point theory. The model's numerical simulations demonstrate that the recommended actions will cause the infected people in the human and non-human populations to disappear.Article Citation - Scopus: 1Caputo-Based Model for Increasing Strains of Coronavirus: Theoretical Analysis and Experimental Design(World Scientific Publ Co Pte Ltd, 2022) Alshomrani, Ali S.; Baleanu, DumitruOne of the most severe and troubling diseases these days is COVID-19 pandemic. The COVID-19 pandemic's dangerous effects are extremely rapid, and infection normally results in death within a few weeks. As a consequence, it is important to delve deeper into the complexities of this elusive virus. In this study, we propose a Caputo-based model for increasing COVID-19 strains. The memory effect and hereditary properties of the fractional variant for the model enable us to fully comprehend the dynamics of the model's features. The existence of unique solution using the fixed-point theorem and Arzela-Ascoli principle as well as the stability analysis of the model by means of Ulam-Hyer stability (UHS) and generalized Ulam-Hyer stability (GUHS) have been discussed. Furthermore, the parameters of the model are estimated using 3 months data points chosen from Nigeria using the nonlinear least-squares technique. The best-suited parameters and the optimized Caputo fractional-order parameter a are obtained by running simulations for both models. The proposed model is shown to comprehend the dynamical behavior of the virus better than the integer-order version. In addition, to shed more light on the model's characteristics, various numerical simulations are performed using an efficient numerical scheme.Article Citation - WoS: 108Citation - Scopus: 122A New Analysis of Fractional Fish Farm Model Associated With Mittag-Leffler Kernel(World Scientific Publ Co Pte Ltd, 2020) Kumar, Devendra; Baleanu, Dumitru; Singh, JagdevIn this paper, we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order. The model is constituted with the group of non-linear differential equations having nutrients, fish and mussel. We have included discrete kind gestational delay of fish. The solution of fish farm model is determined by employing homotopy analysis transforms method (HATM). Existence of and uniqueness of solution are studied through Picard-Lindelof approach. The influence of order of new non-integer order derivative on nutrients, fish and mussel is discussed. The complete study reveals that the outer food supplies manage the behavior of the model. Moreover, to show the outcomes of the study, some numerical results are demonstrated through graphs.