New results involving Airy polynomials, fractional calculus and solution to generalized heat equation
Journal: NEW TRENDS IN MATHEMATICAL SCIENCES (Vol.3, No. 4)Publication Date: 2015-12-01
Authors : Arman Aghili;
Page : 133-143
Keywords : Keywords: Fractional partial differential equationsş heat equations Kd.V equations Airy polynomials Riemann ? Liouville fractional derivative.;
- New results involving Airy polynomials, fractional calculus and solution to generalized heat equation
- On certain fractional calculus operators involving generalized Mittag-Leffler function
- Nonhomogeneous Generalized Multi-Term Fractional Heat Propagation and Fractional Diffusion-Convection Equation in Three-Dimensional Space
- Boundary-value problems for fractional heat equation involving Caputo-Fabrizio derivative
- Fractional calculus; numerical solution of nonlinear fractional differential equations; Grümwald-Letnikov, Riemann-Liouville, Caputo, Dynamics
Abstract
Abstract The main object of this paper is to demonstrate how we can make significant progress in treating a variety of problems in the theory of partial fractional differential equations by combining theory of special functions and operational methods. In this article, it is shown that the combined use of integral transforms and special functions provides a powerful tool to solve certain type of fractional PDEs and generalized heat equation. Constructive examples are also provided.
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