### SOLUTIONS FOR THE FRACTIONAL MATHEMATICAL MODELS OF DIFFUSION PROCESS

Süleyman Çetinkaya, Mine Aylin Bayrak, Ali Demir, Dumitru Baleanu

DOI Number
https://doi.org/10.22190/FUMI210218010C
First page
103
Last page
120

#### Abstract

In this research we present two new approaches with Laplace transformation to form the truncated solution of space-time fractional differential equations (STFDE) with mixed boundary conditions. Since order of the fractional derivative of time derivative is taken between zero and one we have a sub-diffusive differential equation. First, we reduce STFDE into either a time or a space fractional differential equation which are easier to deal with. At the second step the Laplace transformation is applied to the reduced problem to obtain truncated solution. At the final step using the inverse transformations, we get the truncated solution of the problem we consider it. Presented examples illustrate the applicability and power of the approaches, used in this study.

#### Keywords

Laplace transform, Liouville-Caputo derivative, time-space fractional differential equations.

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DOI: https://doi.org/10.22190/FUMI210218010C

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