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 titled problem of coupled thermoelasticity for porous structure has been solved with an instantaneous heat source acting on a plane area in an unbounded medium. The basic equations of thermoelasticity, after being converted into a one-dimensional form, have been written in the form of a vector-matrix differential equation and solved by the eigenvalue approach for the field variables in the ...

Abstract: Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag–Leffler functio...

Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems. To facilitate formal analysis of these systems, we present the formalization of Laplace transform using the multivariable calculus theories of HOL-Light. In particular, we use integral, differentia...

In this paper, we apply the Laplace decomposition method to obtain a series solutions of the Burgers-Huxley and Burgers-Fisher equations. The technique is based on the application of Laplace transform to nonlinear partial differential equations. The method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...