The multidimensional Exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional Exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a Poisson operational matrix. Then we reduce our equation to a linear lower triangular system by constant, Wiener and Poisson operational matrices. Finally using the forward substitution method, we obtain an approximate answer with the convergence rate of O(h). Moreover, we illustrate the accuracy of the proposed method with a 95% confidence interval by some numerical examples.

Fuzziness is ever presented in real life decision making problems. In this paper, we adapt the pessimistic approach to study a pair of linear primal-dual problem under intuitionistic fuzzy (I-fuzzy) environment and prove certain duality results. We generate the duality results using Exponential membership and non-membership functions to represent the decision maker's satisfaction and dissatisfaction level. Further, two numerical examples have been given. In each of these illustrations, varying the values of the shape variables in the Exponential membership functions, various nonlinear optimization problems have been constructed, analyzed and solved. The duality gaps for all these optimization problems have been computed and compared with the duality gap under the linear membership function. We found that these gaps for the I-fuzzy linear primal-dual pair under the Exponential membership functions are smaller as compared with the linear membership functions. The main advantage of using the Exponential membership function is that it has the exibility of altering the values of the shape parameters (as per the decision-maker's satisfaction). Finally, with the help of a suitable ranking defuzzification function, we have extended our approach to the I-fuzzy linear problem with fuzzy parameters and fuzzy constraints.

The present research aims to find a precise method for the wu-zhang system on scattered long waves, which can be a positive step for physical science in dealing with the structure of scattered waves and provide 3D diagrams for further studies of other sciences.

The central topic of the present article is the investigation of solutions of nonlinear fractional partial differential models (NFPDDEs) using the generalized-Exponential-rational-function (GEERAF) Method. In this regard, the jumarie's modified-riemann-liouville (JMRL) derivative has been used to convert the proposed model into ordinary differential-difference model (ODDEM). This efficient proposed method can be used as a replacement for generating novel types of solutions to NFPDDEs in Scientific issues. According to the scientific literature, our findings have not been published before in any other sources.

Various industrial sectors require highly specialized and efficient materials for applications in fields such as the military, aeronautics, aerospace, and mechanical and civil engineering. Composite materials that meet the stringent requirements across these domains have become prominent, often serving as structural components and requiring precise mathematical modeling. Zigzag (ZZ) and Layerwise (LW) theories are commonly used for laminated-beam structural analysis. Although the LW theory provides superior accuracy, it suffers from an increase in unknowns as the number of layers grows. Conversely, the ZZ theory is less computationally intensive and less accurate. This study proposes an Exponential high-order zigzag function with a unified kinematic formulation to enhance the accuracy of the ZZ theory. The results were compared with those of existing models and demonstrated excellent agreement with the reference solutions, irrespective of the layer count or slenderness index, making it a more efficient choice for laminated-beam analysis.

Magnetic Resonance (MR) images have many applications in medical science and play an essential role in the diagnosis and treatment of diseases. However, unavoidable artifacts and noise reduce the resolution of these images. In this paper,  we propose a hybrid noise reduction framework using the wavelet transform, the Exponential function thresholding, and the Wiener filter. In particular, we first employ the Genetic algorithm to optimize the Exponential function coefficient. Furthermore, we adopt the Winner filter to increase the robustness of the proposed scheme against different types of noise, such as Gaussion and Rician noise. Some common performance measures, such as Mean Square Error (MSE) and Peak Signal-to-Noise-Ratio (PSNR), have been used to evaluate the performance of the proposed method compared to existing counterparts. The results show that the performance of the proposed hybrid method is better than the existing methods, such as universal thresholding and plain Exponential function thresholding. For example, for human brain images with Gaussian noise, the obtained PSNR using the proposed method is 53.3947, while the PSNR value is 51.7532 using the universal threshold. Moreover, the results indicate that by using the Winner filter, we can effectively control the robustness against noise and image blurring.