On Solutions of Fractional Telegraph Model with Mittag-Leffler Kernel

In this paper, we research the fractional telegraph equation with the Atangana-Baleanu-Caputo derivative. We use the Laplace method to find the exact solution of the problems. We construct the difference schemes for the implicit finite method. We prove the stability of difference schemes for the problems by the matrix method. We demonstrate the accuracy of the method by some numerical experiments. The obtained results confirm the accuracy and effectiveness of the proposed method. Additionally, the numerical results demonstrate that the expected physical properties of the model are also observed.

Combining Finite Element and Analytical methods to Contact Problems of 3D Structure on Soft Foundation

The computational efficiency and nonconvergence of the iteration are two main difficulties in contact problems, especially in the creep of the foundation. This paper proposes a method to analyze the structural soft foundation system affected by time. The methodology is an explicit method, combining the finite element method with the analytical method. The creep deformation of soft foundation is obtained based on Laplace transforms. The structural deformation contains the statically determinate structural deformation and rigid body displacement, solved by the finite method. The contact forces are calculated by the deformation coordination equations and equilibrium equations. The methodology is validated through augmented Lagrangian (AL) method. The results can clearly illustrate the local disengagement phenome, greatly overcome the nonconvergence of the iteration, and significantly improve computing efficiency.

Using Difference Scheme Method to the Fractional Telegraph Model with Atangana-Baleanu-Caputo Derivative

The fractional telegraph partial differential equation with fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. Laplace method is used to find the exact solution of this equation. Stability inequalities are proved for the exact solution. Difference schemes for the implicit finite method are constructed. The implicit finite method is used to deal with modelling the fractional telegraph differential equation defined by Caputo fractional of Atangana-Baleanu (AB) derivative for different interval. Stability of difference schemes for this problem is proved by the matrix method. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.

Intelligent Computing Based Formulas to Predict the Settlement of Shallow Foundations on Cohesionless Soils

Introduction: Although it is a regular duty of geotechnical engineers to evaluate how much shallow foundation settles in the granular soil, there is no well-approved formula for this task. The intent of this research is to develop a formula that is adequately simple to be used in routine geotechnical engineering work but complete enough to address the behavior of granular soil associated with the settlement issue. Methods: Cone penetration test and foundation load test data were used to generate a formula that can predict the settlement. Genetic Programming (GP) based Symbolic Regression (GP-SR) and artificial neural networks were used to develop an optimized formula. Settlements were also calculated using the finite method and compared to the results of the developed formula. Results and Conclusion: Two formulas were developed using SR, and several models were developed using ANN. ANN model 1 has the highest R2 value (0.93) and the lowest MSE (0.16) among all developed ANN and GP-SR models. FEM settlements were almost double the measured ones in some instances.