<b>The Inverse Nodal problem for the fractional diffusion equation

Abstract

ABSTRACT. In this paper, on a general finite interval, the inverse problem of recovering the potential function for a fractional diffusion equation with new spectral parameter, called the nodal point, is given. Furthermore, using Mittag Leffler function, asymptotic formulas for nodal points and nodal length for a fractional diffusion equation are also found.

On abstract Cauchy problems in the frame of a generalized Caputo type derivative

“…Nowadays, fractional derivatives have been begun to be applied to real world modeling problems ( vertical motion of a falling body problem in a resistant medium and the Malthusian growth equation,.., etc.) and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one or more variables, one can see, [15,16,17,18,19,20]. Some of the most prominent examples are given in a book by Oldham and Spanier [21] (diusion processes) and the classic papers of Bagley and Torvik [22], and Caputo and Mainardi [23] (these two papers dealing with the modeling of viscoelastic materials).…”

Novel Fractional Models Compatible with Real World Problems

“…Very recently, Jarad et al [1] have introduced a new fractional derivative called the Liouville-Caputo fractional conformable derivative. Nowadays, fractional derivatives have been begun to be applied to real world modeling problems [2][3][4][5][6][7][8]. However, many new fractional derivative definitions have been introduced in recent years.…”

β−type fractional Sturm‐Liouville Coulomb operator and applied results

“…[23][24][25][26][27] New approaches are produced on fractional S-L problems in Said Grace et al, Ylmazer, Cabrera et al, Bas, Klimek and Agrawal, and Qi and Chen. [28][29][30][31][32][33] In this study, we take into consideration the modified fractional Hilfer S-L Coulomb problem. Xu and Agrawal defined modified fractional Hilfer derivative in a previous study.…”

“…The direct problems for S‐L operator, both in the regular and singular case, has been considered by numerous studies in Johnson, Zettl, Amrein et al, Kreyszig, and Levitan and Sargsjan . New approaches are produced on fractional S‐L problems in Said Grace et al, Ylmazer, Cabrera et al, Bas, Klimek and Agrawal, and Qi and Chen …”