Jñānābha‎ > ‎Special Issue 2018‎ > ‎

Jñānābha‎ Special Issue (2018), 61-71

ON A FRACTIONAL TIME DERIVATIVE AND MULTI-DIMENSIONAL SPACE EVOLUTION BESSEL STURM LIOUVILLE DIFFUSION AND WAVE PROBLEM
By
1Hemant Kumar and 2Surya Kant Rai
1&2Department of Mathematics
D. A-V. (Postgraduate) College Kanpur-208001, Uttar Pradesh, India
E-mail:
1palhemant2007@rediffmail.com, 2 suryakantrai@gmail.com
(Received : November 24, 2017 ; Revised: October 18, 2018)

Abstract


In this work, we formulate a fractional time derivative and one dimensional space evolution initial value diffusion and wave problem and then, generalize it in multidimensional space and with the fractional time derivative diffusion and wave initial and boundary values problems. Again, we discuss their solutions and special cases as an application of Bessel Sturm Liouville problem and by Duhamel principle.

2010 Mathematics Subject Classification: 26A33, 35M33, 35M12, 44A30.
Keywords and phrases: Caputo fractional derivative, multi-dimensional space and fractional time derivative, diffusion-wave problem, initial and boundary values, Bessel Sturm Liouville problems, Duhamel principle