Due to such wide possibilities fractional-order model application, a number of methods for the construction of exact analytical solutions to FDEs
have been developed.
In a case involving termination of parental rights, Interest of A.K.A.-C., (57) the court took judicial notice of two abuse and neglect cases and one criminal case fde
of the mother, whose rights were at issue.
For this reason, we improve the above ODE and FDE
models by proposing a new fractional order model that describes the interactions between susceptible host cells, viral particles, and the humoral immune response mediated by the antibodies; that is,
Further studies demonstrated that granulysin is strongly expressed in patients with drug-induced FDE
, DRESS/DIHS, and SJS/TEN but not MPE [136-138].
This study showed maculopapular rash as the most common reaction (26.1%) followed by FDEs
and erythematous rash.
Based on these operational matrices, some approximate methods for numerical solutions to FDEs
have been developed (we refer to [34-36] and the references therein).
During the last three decades, fractional order differential equations (FDEs
) have played an important role in modelling many phenomena in engineering [1, 2], applied sciences [3-6], and biological systems [7, 8].
Though many analytic approaches, such as the Fourier transform method, the Mellin transform method, and the Laplace transform methods, have been used to seek the closed-form solutions , there are few available analytical closed-form solutions for fractional differential equations (FDEs
Therefore, utilizing the general Hopfbifurcation theorem for functional differential equations (FDEs
) as given in Hale , we obtain the following results for system (6).
The 30-day mortality and readmission measures came from the CMS's Acute Myocardial Infarction Heart Failure fde
. The PSI and IQIs came from the CMS's Reporting Hospital Quality Data for Annual Payment Update fdes
Different indices for Zipf distribution affect requests from different hot and cold files, while the index [theta] = log A/100 log B/100, means A percent of all accesses were directed to B percent of fdes
. In generally, we set the value of [theta] as 1.8.
We have introduced four problems that use the well-established Grunwald-Letnikov scheme (and some of its descendants), as a sample of emerging mathematical models that rely on FDEs
. We derived the discrete linear systems and matrix Sylvester-type equations that represent the discretized version of the space-, time- and space-time-fractional derivative for both constant and variable coefficients.