An Investigation of Generalized Fuzzy Integral Ro-Transform
Roaa Hameed Hasan, Ameera Nema Alkiffai · Mathematical Modelling and Engineering Problems · 2023
Dueof its numerous and significant applications in a variety of industries, fuzzy differential equations have been applied in various fields during the past few decades.Fuzzy integral transforms are the simplest and most widely used mathematical techniques for solving differential, partial, and integral equations, and we presented this paper in order to keep up with the field's rapid development and progress in the area of fuzzy differential equations.Our research will be restricted to the solution of fuzzy differential equations of the first order.Under certain conditions, fuzzy differential equations may be represented as a dynamical system model.In this paper, generalized differentiability of the fuzzy Ro-transform (FRT) and various R-transform features are proven.A generic formula for the nth-order fuzzy derivative is then produced using highly generalized H-differentiability principles, starting with a formula for the thirdorder fuzzy derivative.The effectiveness of this fuzzy Ro-transform is then demonstrated using a real-world example (the liquid tank system) to highlight the initial value problem.Due of its numerous and significant applications in a variety of industries, fuzzy differential equations have been applied in various fields during the past few decades.Fuzzy integral transforms are the simplest and most widely used mathematical techniques for solving differential, partial, and integral equations, and we presented this paper in order to keep up with the field's rapid development and progress in the area of fuzzy differential equations.Our research will be restricted to the solution of fuzzy differential equations of the first order.Under certain conditions, fuzzy differential equations may be represented as a dynamical system model.In this paper, generalized differentiability of the fuzzy Ro-transform (FRT) and various R-transform features are proven.A generic formula for the nth-order fuzzy derivative is then produced using highly generalized H-differentiability principles, starting with a formula for the third-order fuzzy derivative.The effectiveness of this fuzzy Ro-transform is then demonstrated using a real-world example (the liquid tank system) to highlight the initial value problem.