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Existence and uniqueness of solutions for nonlinear Katugampola fractional differential equations

Basti Bilal, Arioua Yacine, Benhamidouche Nouredine

Journal of Mathematics and Applications

2019

Vol. 42

35--61

The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach fixed point theorems. For applications purposes, some examples are provided to demonstrate the usefulness of our main results.

Use of fractional calculus in modeling of heat transfer process through external building partitions

Szymanek E.

Acta Innovations

2018

no. 27

61--70

This paper is devoted to experimental and numerical studies of heat distribution in an external building bulkhead. It analyzes the variation of temperature across the width of the bulkheads including the impact of changing external conditions. Mathematical model used in the research is formulated based on a fractional differential equation, which was proven to be a useful tool for describing this type of process in previous paper. Numerical results are compared with experiment data for different bulkhead configurations.

Numerical solutions to integral equations equivalent to differential equations with fractional time

Bandrowski B., Karczewska A., Rozmej P.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 2

261-269

This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.

Analysis of fundamental solutions to fractional diffusion-wave equation in polar coordinates

Povstenko Y.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2009

Vol. 14

97-104

The diffusion-wave equation is a mathematical model of a wide range of important physical phenomena. The first and second Cauchy problems and the source problem for the diffusion-wave equation are considered in cylindrical coordinates. The Caputo fractional derivative is used. The Laplace and Hankel transforms are employed. The results are illustrated graphically.