Premium
Existence and uniqueness of analytical solution of time‐fractional Black‐Scholes type equation involving hyper‐Bessel operator
Author(s) -
Zhang Kangqun
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7177
Subject(s) - mathematics , bessel function , uniqueness , eigenfunction , type (biology) , operator (biology) , mathematical analysis , kernel (algebra) , gravitational singularity , hermite polynomials , inverse problem , pure mathematics , ecology , biochemistry , eigenvalues and eigenvectors , physics , chemistry , repressor , quantum mechanics , gene , transcription factor , biology
In this paper, we consider direct problem and inverse source problem of time‐fractional Black‐Scholes type model involving hyper‐Bessel operator. Analytical solutions to these problems are constructed based on appropriate eigenfunction expansion and Erdélyi‐Kober fractional integrals whose kernel has double singularities; then, existence and uniqueness are established. At last, the results are demonstrated by explicit solutions of some examples using appropriate choice of the given data.