Novel Analysis of Fuzzy Physical Models by Generalized Fractional Fuzzy Operators

The present article correlates with a fuzzy hybrid technique combined with an iterative transformation technique identified as the fuzzy new iterative transform method. With the help of Atangana-Baleanu under generalized Hukuhara differentiability, we demonstrate the consistency of this method by achieving fuzzy fractional gas dynamics equations with fuzzy initial conditions. The achieved series solution was determined and contacted the estimated value of the suggested equation. To confirm our technique, three problems have been presented, and the results were estimated in fuzzy type. The lower and upper portions of the fuzzy solution in all three examples were simulated using two distinct fractional orders between 0 and 1. Because the exponential function is present, the fractional operator is nonsingular and global. It provides all forms of fuzzy solutions occurring between 0 and 1 at any fractional-order because it globalizes the dynamical behavior of the given equation. Because the fuzzy number provides the solution in fuzzy form, with upper and lower branches, fuzziness is also incorporated in the unknown quantity. It is essential to mention that the projected methodology to fuzziness is to confirm the superiority and efficiency of constructing numerical results to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

Mathematical simulation analysis of optimal detection of shot-putters’ best path

In order to consider many uncertain factors in the process of shot-put, a fuzzy optimisation model of shot-put is proposed. With the help of fuzzy anthropometric data and strength data, the model calculates the fuzzy solution set of the athlete's best throwing mode and throwing distance with a known probability distribution, which reflects the actual process of shot throwing better than the non-fuzzy optimisation model. Then, using MATLAB6 software, the program design of the model solving and the user interface of optimisation software are developed, which realises fast calculation and good user interaction function. Finally, the actual measurement data of university shot-putters are used to verify the feasibility and effectiveness of the fuzzy optimisation model.

A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers

Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method.

Generalized Hukuhara Conformable Fractional Derivative and its Application to Fuzzy Fractional Partial DifferentialEquations

The main focus of this paper is to develop an efficient analytical method to obtain the traveling wave fuzzy solution for the fuzzy generalized Hukuhara conformable fractional equations by considering the type of generalized Hukuhara conformable fractional differentiability of the solution. To achieve this, the fuzzy conformable fractional derivative based on the generalized Hukuhara differentiability is defined, and several properties are brought on the topic, such as switching points and the fuzzy chain rule. After that, a new analytical method is applied to find the exact solutions for two famous mathematical equations: the fuzzy fractional Wave equation and the fuzzy fractional Diffusion equation. The present work is the first report in which the fuzzy traveling wave method is used to design an analytical method to solve these fuzzy problems. The final examples are asserted that our new method is applicable and efficient.

Solving Complex Fuzzy Linear Matrix Equations

In this paper, a kind of complex fuzzy linear matrix equation A X ˜ B = C ˜ , in which C ˜ is a complex fuzzy matrix and A and B are crisp matrices, is investigated by using a matrix method. The complex fuzzy matrix equation is extended into a crisp system of matrix equations by means of arithmetic operations of fuzzy numbers. Two brand new and simplified procedures for solving the original fuzzy equation are proposed and the correspondingly sufficient condition for strong fuzzy solution are analysed. Some examples are calculated in detail to illustrate our proposed method.

Semi-Analytical Solutions for Fuzzy Caputo–Fabrizio Fractional-Order Two-Dimensional Heat Equation

In the analysis in this article, we developed a scheme for the computation of a semi-analytical solution to a fuzzy fractional-order heat equation of two dimensions having some external diffusion source term. For this, we applied the Laplace transform along with decomposition techniques and the Adomian polynomial under the Caputo–Fabrizio fractional differential operator. Furthermore, for obtaining a semi-analytical series-type solution, the decomposition of the unknown quantity and its addition established the said solution. The obtained series solution was calculated and approached the approximate solution of the proposed equation. For the validation of our scheme, three different examples have been provided, and the solutions were calculated in fuzzy form. All the three illustrations simulated two different fractional orders between 0 and 1 for the upper and lower portions of the fuzzy solution. The said fractional operator is nonsingular and global due to the presence of the exponential function. It globalizes the dynamical behavior of the said equation, which is guaranteed for all types of fuzzy solution lying between 0 and 1 at any fractional order. The fuzziness is also included in the unknown quantity due to the fuzzy number providing the solution in fuzzy form, having upper and lower branches.

Fuzzy Sawi Decomposition Method for Solving Nonlinear Partial Fuzzy Differential Equations

The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition method. For this purpose, two new theorems for fuzzy Sawi transformation regarding fuzzy partial gH-derivatives are introduced. The use of convex symmetrical triangular fuzzy numbers creates symmetry between the lower and upper representations of the fuzzy solution. To demonstrate the effectiveness of the method, a numerical example is provided.

On numerical approximation of Atangana-Baleanu-Caputo fractional integro-differential equations under uncertainty in Hilbert Space

The paper uses the Atangana-Baleanu-Caputo(ABC) fractional operator for an effective advanced numerical-analysis approach to apply in handling various classes of fuzzy integro-differential equations of fractional order along with uncertain constraints conditions. We adopt the fractional derivative of ABC under generalized H-differentiability(g-HD) that uses the Mittag-Leffler function as a nonlocal kernel to better describe the timescale in fuzzy models and reduce complicity of numerical computations. Towards this end, the applications of reproducing kernel algorithm are extended for solving classes of linear and non-linear fuzzy fractional ABC Volterra-Fredholm integro-differential equations. The interval parametric solutions are provided in term of rapidly convergent series in Sobolev spaces. Based on the characterization theorem, preconditions are established to characterize the fuzzy solution in a coupled equivalent system of crisp ABC integro-differential equations. The viability and efficiency of the putative algorithm are tested by solving several fuzzy ABC Volterra-Fredholm types examples under the g-HD. The achieved numerical results are given for both classical Caputo and ABC fractional derivatives to show the effect of the ABC derivative on the interval parametric solutions of the fuzzy models, which reveal that the present method is systematic and suitable for dealing with fuzzy fractional problems arising in physics, technology, and engineering.