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    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.
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    The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications
    (Hindawi Ltd, 2024) Allahviranloo, T.; Shahryari, M. R. Balooch; Sedaghatfar, O.; Shahriari, M. R.; Saadati, R.; Noeiaghdam, S.; Fernandez-Gamiz, U.
    In this paper, we are thus motivated to define and introduce the extended fuzzy-valued convex functions that can take the singleton fuzzy values -infinity similar to and +infinity similar to at some points. Such functions can be characterized using the notions of effective domain and epigraph. In this way, we study important concepts such as fuzzy indicator function and fuzzy infimal convolution for extended fuzzy-valued functions. Finally, we introduce the concept of directional generalized derivative for extended above functions and its properties. Eventually, we give a practical example that will illustrate well the directional g-derivative for the extended fuzzy-valued convex function.