On the challenge of identifying space dependent coefficient in space-time fractional diffusion equations by fractional scaling transformations method

Authors : Mine Aylin BAYRAK, Ali DEMİR

Pages : 132-145

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Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :In this study, we get over the challenge of recovering unknown space dependent coefficient in space-time fractional diffusion equations by means of fractional scaling transformations method. Fractional differential equation is given in the sense of the conformable fractional derivative having substantial properties. By these properties and fractional scaling transformations method the fractional problem is reduced into integer order problem which allows us to tackle the problem better. Then we establish the solution and unknown coefficient of the reduced problem. Later, by employing inverse transformation, the solution and unknown coefficient of the fractional problem are obtained. Finally, some examples are presented to illustrate the implementation and effectiveness of the method.
Keywords : space time fractional diffusion equation, fractional scaling transformation method, conformable fractional derivative