A fractal-fractional sex structured syphilis model with three stages of infection and loss of immunity with analysis and modeling

Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator

“… 20 , 21 , 24 For a power law kernel, the fractal–fractional derivative in the Riemann-Liouville sense with order is defined as: where The associated fractal–fractional integral is expressed as follows: …”

“… 20 , 21 , 24 For an exponential decay kernel, the fractal–fractional derivative in the Riemann-Liouville sense with order is defined as: where , and .…”

“… 20 , 21 , 24 For a Mittag-Leffler kernel, the fractal–fractional derivative in the Riemann-Liouville sense with order is defined as: where , is the Mittag-Leffler function and is a normalization function.…”

“…Power rule, exponential purpose, or Mittag-Leffler purpose are examples of local derivatives that are necessary in Caputo-type situations; earlier work 20 introduced fractal–fractional operators, which combine fractal and fractional calculus. When describing real-world data and modeling mathematical concepts, fractal–fractional operators work better 21 – 27 . Using power law kernels and fractal–fractional operators, a new model was created 28 for a particular type of influenza virus.…”