Browsing by Author "Rahaman,M."

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Citation Count: 3
A Fuzzy Fractional Power Series Approximation and Taylor Expansion for Solving Fuzzy Fractional Differential Equation
(Elsevier Inc., 2024) Singh,P.; Salahshour, Soheıl; Rahaman,M.; Salahshour,S.; Mondal,S.P.
Fuzzy fractional differential has the strength to capture the senses of memory and uncertainty simultaneously involved in dynamical systems. However, a solution for fuzzy fractional differential equations is not always found regularly. This paper discusses a numerical solution approach for the fuzzy fractional differential equation using power series approximation with a fuzzy fractional counterpart of Taylor's theorem. Caputo's definition of the fractional derivative and generalized Hukuhara difference are used to describe the fuzzy differential equation in this paper. Utilization of the generalized Hukuhara difference for the fuzzy valued function ensures the uniqueness and boundedness of the fuzzy solution in parametric form. © 2024 The Author(s)
Citation Count: 0
Metric Space and Calculus of Type-2 Interval-Valued Functions
(World Scientific, 2024) Salahshour, Soheıl; Das,M.; Alam,S.; Salahshour,S.; Mondal,S.P.
This paper attempts an extensive study on metric space and calculus under Type 2 interval uncertainty. Type 2 interval generalizes interval uncertainty considering both ends of the interval number to be imprecise. Type 2 interval philosophy was introduced in the literature with optimization perspectives. We prioritize the study of Type 2 interval-ruled dynamical systems. The concerns necessitate an extensive introduction of metric space and calculus for Type 2 interval-valued functions. We investigate several fundamental properties of metric space in the contemporary of Type 2 interval setting. After significant findings in differential calculus using generalized Hukuhara difference of Type 2 interval numbers, a detailed and novel manifestation of integral calculus including Riemann and Lebesgue senses is also done in this paper. We also provide hints for possible mathematical modelings of real-world scenarios using Type 2 interval-ruled uncertain decision realm. © 2024 World Scientific Publishing Company.