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    2-Absorbing Vague Weakly Complete ?-Ideals in ?-Rings
    (Mdpi, 2023) Onar, Serkan; Hila, Kostaq; Etemad, Sina; Akgül, Ali; De la sen, Manuel; Rezapour, Shahram
    The aim of this study is to provide a generalization of prime vague Gamma-ideals in Gamma-rings by introducing non-symmetric 2-absorbing vague weakly complete Gamma-ideals of commutative Gamma-rings. A novel algebraic structure of a primary vague Gamma-ideal of a commutative Gamma-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Gamma-ideals of Gamma-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Gamma-ideals and 2-absorbing Gamma-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Gamma-ideal of a Gamma-ring and 2-absorbing K-vague Gamma-ideal of a Gamma-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Gamma-ring of R induced by a 2-absorbing vague weakly complete Gamma-ideal of a 2-absorbing Gamma-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Gamma-ideal.
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    Öğe
    On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique
    (Amer Inst Mathematical Sciences-Aims, 2023) Bouazza, Zoubida; Souhila, Sabit; Etemad, Sina; Souid, Mohammed Said; Akguel, Ali; Rezapour, Shahram; De la Sen, Manuel
    This paper studies the existence of solutions for Caputo-Hadamard fractional nonlinear differential equations of variable order (CHFDEVO). We obtain some needed conditions for this purpose by providing an auxiliary constant order system of the given CHFDEVO. In other words, with the help of piece-wise constant order functions on some continuous subintervals of a partition, we convert the main variable order initial value problem (IVP) to a constant order IVP of the Caputo-Hadamard differential equations. By calculating and obtaining equivalent solutions in the form of a Hadamard integral equation, our results are established with the help of the upper-lower-solutions method. Finally, a numerical example is presented to express the validity of our results.
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    Öğe
    On the fractal-fractional Mittag-Leffler model of a COVID-19 and Zika Co-infection
    (Elsevier, 2023) Rezapour, Shahram; Asamoah, Joshua Kiddy K.; Etemad, Sina; Akgul, Ali; Avci, Ibrahim; El Din, Sayed M.
    The World Health Organization declared COVID-19 a global pandemic in March 2020, which had a significant impact on global health and economies. There have been several Zika outbreaks in different regions such as Africa, Southeast Asia, and the Americas. Therefore, it is essential to study the dynamics of these two diseases, taking into account their memory and recurrence effects. A new fractal-fractional hybrid Mittag-Leffler model of COVID-19 and Zika co-dynamics is designed and studied to evaluate the effects of COVID-19 on Zika and vice-versa. The stability analysis of the local asymptotic type at disease-free equilibrium is conducted for the hybrid model. The existence of unique solutions to the model is established via some fixed point results. The fractal-fractional model is proved to be Hyers-Ulam stable. With the help of Newton polynomials, we obtain some numerical algorithms to approximate the solutions of the fractal-fractional hybrid Mittag-Leffler model graphically. The impact of fractional and fractal orders on the dynamics of each of the epidemiological classes is also assessed. In addition, empirical evidence from numerical simulations suggests that implementing measures to contain the transmission of the SARS-CoV-2 virus can significantly contribute to the reduction of co-infections involving the Zika virus. Therefore, it is imperative for healthcare systems to maintain a state of constant vigilance in order to detect any atypical patterns or probable occurrences of co-infections, particularly in areas where both diseases are widespread. Additionally, it is vital to consult the most recent directives provided by health authorities, as our comprehension of diseases may undergo advancements over the course of time.