Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...

The hypergeometric functions are one of the most important and special in mathematics. They generalization exponential functions. Particularly ordinary function 2F1(a, b; c; z) is represented by series a solution to second order differential equation. Similarly, Laplace transform form integral that converts linear equations algebraic equations. This paper aims study convergence some Moreover, r...

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Nahm transform for parabolic connections. . . . . . . . . . . . 3 2. Laplace transform without parabolic structure . . . . . . . 8 3. Meromorphic connections and D-modules. . . . . . . . . . . . 10 4. Minimal parabolic Laplace transform. . . . . . . . . . . . . . . . . 14 5. Proof – outline....

The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., images), thus, limiting its potential application arbitrary in terms of dimensionality structure. This article defines analyzes the properties data-driven F-transform, with focus on construction class membership functions, which are multiscale, local, linearly independent, intrinsic, robust disc...

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...