Jñānābha‎, Vol. 48 (1) (2018), 121-133

ON THREE DIMENSIONAL LEGENDRE STURM LIOUVILLE DIFFUSION AND WAVE PROBLEM GENERATED DUE TO FRACTIONAL TIME DERIVATIVE

Hemant Kumar
Department of Mathematics, D. A-V. (P. G.) College Kanpur-208001 India

Abstract 

In this work, we establish and discuss three dimensional Legendre Sturm Liouville diffusion and wave problem generated due to fractional time derivative and with initial and boundary value conditions. Also, we obtain and analyze its solution by Duhamel principle and verify it by convolution theory. 

MSC 2010:26A33, 35M33, 35M12, 44A30. 
Keywords: Caputo fractional derivative, three dimensional Legendre Sturm Liouville diffusion and wave problem, initial and boundary values, Duhamel principle.