Fractal Logistic Equation

Abstract

In this paper, we give difference equations on fractal sets and their corresponding fractal differential equations. An analogue of the classical Euler method in fractal calculus is defined. This fractal Euler method presets a numerical method for solving fractal differential equations and finding approximate analytical solutions. Fractal differential equations are solved by using the fractal Euler method. Furthermore, fractal logistic equations and functions are given, which are useful in modeling growth of elements in sciences including biology and economics.

On some computational aspects of Hermite & Haar wavelets on a class of nonlinear singular BVPs

“…where R is a gas constant, T is absolute temperature, A, E 0 and T 0 are parameters and n is an integer. Similar to analysis of Chambre [26], we arrive at the following differential equation (1) Ly = −B exp −A…”

“…In this section we apply HeWQA, HeWNA, HWQA and HWNA on proposed model which occurs in exothermic reaction (1). We also solve four other examples from real life and compare solutions of these four methods with exact solutions whenever available.…”

Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions

“…. (11) is analysis aims at extending the application of fractional Taylor series framework to get an accurate analytic series solution of fractional systems (1) and (2). us, if we use the initial data given by (2), D α 0 q(0) � p 0 , as initial truncated series of q(t), so the FPS solution of equation 1can be written by…”

“…On the other hand, the continuous logistic system has a steady population growth rate in the form of Q(t) � p 0 e λt with initial population data p 0 . In addition, the theory of existence and uniqueness of the continuous logistic system in a fractional sense has been presented in the literature; for more details, see [11][12][13][14][15].…”

On solutions of fractal fractional differential equations

“…These operators can be considered as upper classes of differential and integral operators as they can be converted to classical, fractal and fractional differential and integral operators in the limit cases [14,12,22,5,17,11]. For more details see [6,7,15,16,19,4,8,10,18,9,20,21].…”