We investigate the fuzzy fractional European option pricing models in the sense of the fuzzy AtanganaBaleanu derivative in this paper. The paper’s main contribution is the analysis of the existence and uniqueness of the fuzzy European-type option pricing model that provides a fundamental solution. Moreover, we set up a new scheme for approximating solutions of this model based on fuzzy homotopy perturbation transform method. This procedure is used successfully on two examples for finding the solutions

Injury domain method does not let the cracks close to the critical level to start growing and lead to the critical length before the time of periodic visits. Until now, calculation method of the tension in a perforated plate has been assessed in two- or three-dimensional mode by considering the special opening (holes with different geometry). But, the tension calculation in a plate included opening with edge crack presence in three-dimensional mode has not been studied. So, in this study, in addition to the assessment of this mode, calculation method of the tension in the plates including different opening will be assessed. Generally, when the object endures the tensions for a long time, the geometric deformation will be occurred. Used plates in this study are made of isotropic materials. In these materials, when the force is applied, they show the same function in any direction and the direction of applying force has any on effect their treatment. For analyzing the data, the Abaqus software is used. The results of the research show that the kind of the boundary conditions has effect on the value of critical load in the tension and kind of created tension. In the joint-joint boundary conditions, tension critical load increases with length-to-width ratio increase, and local tension occurred in the higher penetration ratio. However, in the joint-open boundary conditions, by increasing the length-to-width ratio, the tension critical load is decreased and in often cases, the tensions are kind of general. According to this, the plates including cavity with bigger dimensions are subjected to local tension in smaller ratios of yielding dimension.