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Öğe Fuzzy approximation of a fractional Lorenz system and a fractional financial crisis(Univ Sistan & Baluchestan, 2023) Aderyani, S. Rezaei; Saadati, R.; Allahviranloo, T.; Abbasbandy, S.; Catak, M.The butterfly effect, the possibility that a small change in initial conditions may have momentous effects, is a concept that was presented by an American mathematician and meteorologist Edward Lorenz. Nearly forty five years ago, he posed a question: does the flap of a butterfly's wings in Brazil set off a tornado in Texas trying to express why it is so difficult to earn a suitable weather forecast. In an experiment, he replaced the initial condition 0.506 with 0.506127. The effect was amazing. Lorenz was the first person who recognizes chaotic theory in the mathematical model of weather. His researches leads to a new field of study not only in mathematics but also in biology, physics, meteorology and so on. In fact, the Lorenz system is a model-driven Rayleigh-Be & PRIME;nard convection. For more details, we refer to [1, 4, 11]. In this paper, we consider the fractional version of the Lorenz system in the sense of the Caputo-Fabrizio derivative, and apply a fuzzy control function with the Mihet-Radu method, to investigate the fuzzy Ulam-Wright stability with the uniqueness of the solution. Also, we investigate the fuzzy Ulam-Wright stability of a financial crisis model presented by Korobeinikov [5], in the sense of h-Hilfer derivative.Öğe A New Numerical Approach for Solving the Fractional Nonlinear Multi-pantograph Delay Differential Equations(Springer Int Publ Ag, 2023) Hajishafieiha, J.; Abbasbandy, S.; Allahviranloo, T.The numerical solution of the fractional nonlinear multi-pantograph delay differential equations is investigated by a new class of polynomials. These polynomials are equipped with an unknown auxiliary parameter a, which is obtained by using the collocation and least-squares methods. In this paper, the numerical solution of the fractional nonlinear multi-pantograph delay differential equation is displayed in the truncated series form. The existence and uniqueness of the solution and the error analysis are also investigated in this article. In four examples, the numerical results of the present method have been compared with other methods. For the first time, a-polynomials are used in this article to numerically solve the fractional nonlinear multi-pantograph delay differential equations, and accurate approximations have been displayed.Öğe Solving fully linear programming problem based on Z-numbers(Univ Sistan & Baluchestan, 2023) Joghataee, M.; Allahviranloo, T.; Lotfi, F. Hosseinzadeh; Ebrahimnejad, A.; Abbasbandy, S.; Amirteimoori, A.; Catak, M.Generally exploring the exact solution of linear programming problems in which all variables and parameters are Znumbers, is either not possible or difficult. Therefore, a few numerical methods to find the numerical solutions do act an important role in these problems. In this paper, we concentrate on introducing a new numerical method to solve such problems based on the ranking function. After proving the necessary theories, for more illustrations and the correctness of the topic, some theoretical and practical examples are also provided. Finally, the results obtained from the proposed method have been compared with some existing methods.
