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

100%

Szymanek E.

tom 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

86%

Bandrowski B. , Karczewska A. , Rozmej P.

2010

tom 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.

Existence results of noninstantaneous impulsive fractional integro-differential equation

72%

Kataria H. R. , Patel P. H. , Shah V.

2020

tom Vol. 53, nr 1

373--384

Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.