ESTIMATED SOLUTIONS OF GENERALIZED AND MULTIDIMENSIONAL CHURCHILL’S DIFFUSION PROBLEMS
R. C. Singh Chandel* and Hemant Kumar
*Former Head, Department of Mathematics
D. V. Postgraduate College Orai- 285001, Uttar Pradesh, India
Department of Mathematics
D. A-V. Postgraduate College Kanpur - 208001, Uttar Pradesh, India
(Received : July 02, 2020 ; Revised: September 17, 2020)
In this paper to define a generalized Churchill’s diffusion problem, we first extend the Churchill’s diffusion problem. Then, we derive some of estimated and computational formulae of its solution. Further, we present a multidimensional Churchill’s diffusion problem consisting of multidimensional Euler space derivatives and Caputo time fractional derivative. Then, on imposing certain boundary values, we obtain its solution and derive its many estimated formulae.
2010 Mathematics Subject Classifications: 26A33, 46A45, 35K58, 33E12.
Keywords and phrases: Multidimensional Euler space derivatives, Caputo time fractional derivative, Laplace transformation, a generalized Churchill’s diffusion problem, a multidimensional Churchill’s diffusion problem, estimation formulae.
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