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Start date: 2020End date: 2026Author: search.filters.author.Salahshour, SoheilType: search.filters.itemtype.Book Chapter

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    Arbitrary Order Differential Equations with Fuzzy Parameters
    (wiley, 2020) Allahviranloo, Tofigh A.; Salahshour, Soheil; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey; Salahshour, Soheil, Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    In the last decades, some generalization of theory of ordinary differential equations has been considered to the arbitrary order differential equations by many researchers, the so-called theory of arbitrary order differential equations (often called as fractional order differential equations [FDEs]). Because of the ability for modeling real phenomena, arbitrary order differential equations have been applied in various fields such as control systems, biosciences, bioengineering, and references therein. In this chapter, the authors propose arbitrary order differential equations with respect to another function using fuzzy parameters (initial values and the unknown solutions). The generalized fuzzy Laplace transform is applied to obtain the Laplace transform of arbitrary order integral and derivative of fuzzy-valued functions to solve linear FDEs. To obtain the large class of solutions for FDEs, the concept of generalized Hukuhara differentiability is applied. © 2025 Elsevier B.V., All rights reserved.
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    Solution Strategy for Fuzzy Fractional Order Linear Homogeneous Differential Equation by Caputo-H Differentiability and Its Application in Fuzzy EOQ Model
    (Springer Science and Business Media Deutschland GmbH, 2022) Rahaman, Mostafijur; Mondal, Sankar Prasad; El Allaoui, Abdelati; Alam, Shariful; Ahmadian, Ali; Salahshour, Soheil; Rahaman, Mostafijur, Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India; Mondal, Sankar Prasad, West Bengal, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, India; El Allaoui, Abdelati, Laboratoire de Mathematiques Appliquees & Calcul Scientique, Université Sultan Moulay Slimane, Beni Mellal, Morocco; Alam, Shariful, Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India; Ahmadian, Ali, Universiti Kebangsaan Malaysia, Bangi, Malaysia; Salahshour, Soheil, Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    This chapter aims to describe a stock dependent memory concerned EOQ model in fuzzy uncertain situation. Before developing the EOQ model, a brief theory of fuzzy fractional linear homogeneous differential equation inspired by Caputo H differentiability has been established in this paper. In the fuzzy fractional linear homogeneous differential equation, both the co-efficient and the initial value are assumed to be fuzzy number. © 2021 Elsevier B.V., All rights reserved.