A Method for Solving Initial and Boundary Value Fuzzy differential equations by Mellin Transform

This Paper is included fuzzy concepts of Mellin transform along with its operational properties. Mellin transform method is applicable in fuzzy context. The study involved the proposed techniques for solving initial and boundary value fuzzy differential equations under strongly generalized differentiability concepts.

A Method for Solving Initial and Boundary Value Fuzzy differential equations by Mellin Transform

This Paper is involved fuzzy concepts of Mellin transform along with its properties by proposed methods. The study involved also the proposed techniques for solving initial and boundary value fuzzy differential equations under strongly generalized differentiability concepts.

An Analytical Numerical Method for Solving Fuzzy Fractional Volterra Integro-Differential Equations

The modeling of fuzzy fractional integro-differential equations is a very significant matter in engineering and applied sciences. This paper presents a novel treatment algorithm based on utilizing the fractional residual power series (FRPS) method to study and interpret the approximated solutions for a class of fuzzy fractional Volterra integro-differential equations of order 0<β≤1 which are subject to appropriate symmetric triangular fuzzy conditions under strongly generalized differentiability. The proposed algorithm relies upon the residual error concept and on the formula of generalized Taylor. The FRPS algorithm provides approximated solutions in parametric form with rapidly convergent fractional power series without linearization, limitation on the problem’s nature, and sort of classification or perturbation. The fuzzy fractional derivatives are described via the Caputo fuzzy H-differentiable. The ability, effectiveness, and simplicity of the proposed technique are demonstrated by testing two applications. Graphical and numerical results reveal the symmetry between the lower and upper r-cut representations of the fuzzy solution and satisfy the convex symmetric triangular fuzzy number. Notably, the symmetric fuzzy solutions on a focus of their core and support refer to a sense of proportion, harmony, and balance. The obtained results reveal that the FRPS scheme is simple, straightforward, accurate and convenient to solve different forms of fuzzy fractional differential equations.

Some results on the fundamental concepts of fuzzy set theory in intuitionistic fuzzy environment by using α and β cuts

In this paper we have firstly examined the properties of ? and ? cuts of intuitionistic fuzzy numbers in Rn with the help of well-known Stacking and Characterization theorems in fuzzy set theory. Then, we have studied the generalized Hukuhara difference in intuitionistic fuzzy environment by using the properties of ? and ? cuts and support function. Finally, we have extended the strongly generalized differentiability concept from fuzzy set theory to intuitionistic fuzzy environment and proved the related theorems with this concept.

An efficient analytical-numerical technique for handling model of fuzzy differential equations of fractional-order

This paper adds in our hands a different analytic numeric method to solve a class of fuzzy fractional differential equations (FFDEs) based on the residual power series method (RPSM) under strongly generalized differentiability. The analytic and approximate solutions are provided with the series form according to their parametric form. The new method explained in the current paper has a lot of advantages as follows: First, its nature is global according to the obtainable solutions along with being able to solve numerous problems such as mathematical, physical and engineering ones. Second. It is easily noted that it is precise, needs few efforts to have the required results achieved, alongside being developed for nonlinear problems and cases. As for the third advantage, it can be said that any point in the interval of interest will be possibly picked, in addition, to have the approximate solutions applied. Fourth, the method does not need the variables discretization, also it is not implemented by computational round of errors. At last, the results reached in the current paper show several features concerning the new method such as potentiality, generality and superiority to handle such problems arising in physics and engineering as well.

Fuzzy Sumudu Transform for Solving System of Linear Fuzzy Differential Equations with Fuzzy Constant Coefficients

In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

Soution of fuzzy initial value problems by fuzzy Laplace transform

In this paper we propose a fuzzy Laplace transform to solve fuzzy initial value problem under strongly generalized differentiability concept. The fuzzy Laplace transform of derivative was used to solve Nth-order fuzzy initial value problem. To illustrate applicability of proposed method we plot graphs for different values of r -level sets by using Mathematica Software.

Analytical solutions forfuzzysystem using power series approach

The aim of the present paper is present a relatively new analytical method, called residual power series (RPS) method, for solving system of fuzzy initial value problems under strongly generalized differentiability. The technique methodology provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. The results reveal that the present simulated method is very effective, straightforward and powerful methodology to solve such fuzzy equations.

Existence, Uniqueness, and Characterization Theorems for Nonlinear Fuzzy Integrodifferential Equations of Volterra Type

Existence and uniqueness theorem are the tool which makes it possible for us to conclude that there exists only one solution to a given problem which satisfies a constraint condition. How does it work? Why is it the case? We believe it, but it would be interesting to see the main ideas behind this. To this end, in this paper, we investigate existence, uniqueness, and other properties of solutions of a certain nonlinear fuzzy Volterra integrodifferential equation under strongly generalized differentiability. The main tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. Also, some results for characterizing solution by an equivalent system of crisp Volterra integrodifferential equations are presented. In this way, a new direction for the methods of analytic and approximate solutions is proposed.