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Start date: 2020End date: 2026Type: search.filters.itemtype.Book ChapterAuthor: search.filters.author.Allahviranloo, Tofigh A.

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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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    Uncertainty
    (Springer International Publishing, 2020) Allahviranloo, Tofigh A.; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    In this chapter, we are going to define, introduce and explain many types of uncertainties. © 2019 Elsevier B.V., All rights reserved.
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    Advanced Uncertainty and Linear Equations
    (Springer International Publishing, 2020) Allahviranloo, Tofigh A.; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    In this chapter, first of all we introduced an extended version of uncertainty entitled ‘pseudo-octagonal’ uncertain sets. Then the special cases as ‘pseudo-triangular’ and ‘pseudo-trapezoidal’ are introduced. © 2019 Elsevier B.V., All rights reserved.
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    Uncertain information and linear systems
    (Springer International Publishing, 2020) Allahviranloo, Tofigh A.; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    [No abstract available]
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    Introduction
    (Springer International Publishing, 2020) Allahviranloo, Tofigh A.; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    As for the laws of mathematics refer to reality, they are not certain, and as far as they are certain. © 2019 Elsevier B.V., All rights reserved.
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    Uncertain Linear Systems
    (Springer International Publishing, 2020) Allahviranloo, Tofigh A.; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    In this chapter, we are going to discuss about the uncertain linear system that is involved with any uncertainties. First of all, it should be mentioned that an uncertain linear system is indeed an extension of interval linear system. This is why, we will discuss about the systems involving interval analysis approach. The structure of this chapter is classified to two folds. The first one is about an uncertain linear system with uncertainty in the right hand side and the second section points out fully uncertain linear systems but the folds are not separated completely. © 2019 Elsevier B.V., All rights reserved.
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    On the Z-Numbers
    (Springer, 2020) Allahviranloo, Tofigh A.; Ezadi, Somayeh; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey; Ezadi, Somayeh, Department of Mathematics, Islamic Azad University, Tehran, Iran
    In this chapter, first the Z-number is introduced then calculating operations are defined. Moreover several ranking methods are investigated to order the Z-numbers for using in other appropriate models. To points out one of the application, a regression method based on neural network technique is described in detail. Finally, the initial value problem with Z-number initial value (as a most applicable model) is introduced. © 2020 Elsevier B.V., All rights reserved.
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    Numerical solution of fuzzy fractional differential equations
    (Springer, 2021) Allahviranloo, Tofigh A.; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    In this chapter, first, some numerical methods such as generalized fuzzy fractional Taylor’s expansion and its application entitled fuzzy fractional Euler’s method are presented for fuzzy-valued function in the sense of Caputo differentiability. Then the fuzzy impulsive fractional differential equations are going to be considered for numerically solving by some semi analytically methods. Also the fuzzy fractional differential equation is solved by applying some other derivatives such as ABC derivative by using numerical methods. © 2020 Elsevier B.V., All rights reserved.
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    Applications of fuzzy fractional differential equations
    (Springer, 2021) Allahviranloo, Tofigh A.; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    In general, fractional calculus deals with the generalization of differentiation and integration of non-integer orders. In recent years, fractional calculus has played a significant role in several sciences such as physics, chemistry, biology, electronics, and control theory. © 2020 Elsevier B.V., All rights reserved.
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    Introduction to fuzzy fractional operators and equations
    (Springer, 2021) Allahviranloo, Tofigh A.; Allahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    Uncertainty and hesitation always live with us and this is the reality. All human beings are accustomed to doubting of everything around them and asking themselves or others why? © 2020 Elsevier B.V., All rights reserved.