Dynamical analysis of a nonlinear fractional cervical cancer epidemic model with the nonstandard finite difference method

Butt, Asma Rashid; Ahmad Saqib, Aitzaz; Alshomrani, Ali Saleh; Bakar, Abu; Inc, Mustafa

doi:10.1016/j.asej.2023.102479

Cited by 3 publications

(1 citation statement)

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“…The Grunwald-Letnikov fractional derivatives have been used in numerical analysis to discretize the fractional differential equations. From this year, the non-standard discretization scheme began to be actively studied and applied to fractional differential equations of the non-integer orders in various works [70][71][72][73][74][75][76][77][78][79][80][81][82][83][84]. However, the disadvantages of this scheme after generalization for operators of the non-integer order remained almost the same.…”

Section: Introductionmentioning

confidence: 99%

Exact Finite-Difference Calculus: Beyond Set of Entire Functions

Tarasov

2024

Mathematics

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In this paper, a short review of the calculus of exact finite-differences of integer order is proposed. The finite-difference operators are called the exact finite-differences of integer orders, if these operators satisfy the same characteristic algebraic relations as standard differential operators of the same order on some function space. In this paper, we prove theorem that this property of the exact finite-differences is satisfies for the space of simple entire functions on the real axis (i.e., functions that can be expanded into power series on the real axis). In addition, new results that describe the exact finite-differences beyond the set of entire functions are proposed. A generalized expression of exact finite-differences for non-entire functions is suggested. As an example, the exact finite-differences of the square root function is considered. The use of exact finite-differences for numerical and computer simulations is not discussed in this paper. Exact finite-differences are considered as an algebraic analog of standard derivatives of integer order.

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