Maximum principle and its application to multi-index Hadamard fractional diffusion equation

Abstract

This study establishes some new maximum principle which will help to investigate an IBVP for multi-index Hadamard fractional diffusion equation. With the help of the new maximum principle, this paper ensures that the focused multi-index Hadamard fractional diffusion equation possesses at most one classical solution and that the solution depends continuously on its initial boundary value conditions.

An upper-lower solution method for the eigenvalue problem of Hadamard-type singular fractional differential equation

“…However, the Hadamard-type fractional integral and derivative differ from the Riemann-Liouville and the Caputo fractional derivative since the kernels of the Hadamard-type integral and derivative contain logarithmic functions of arbitrary exponent and thus are regarded as a different kind of weakly singular kernels. Thus it is more difficult to explore the existence of solutions for the Hadamard-type fractional differential equations, [2,10,11,21].…”

Study of implicit delay fractional differential equations under anti-periodic boundary conditions

“…In the recent times this has been the hottest and most interesting area of research in mathematics as well as in other scientific and engineering courses. For some historical and recent work, we refer the readers to [1][2][3][4][5][6][7][8][9]. A comprehensive study in the form of a book has been given by Podlubny [10].…”