Abstract
The main objective of this study is to apply the local fractional homotopy analysis method (LFHAM) to obtain the non-differentiable solution of two nonlinear partial differential equations of the biological population model on Cantor sets. The derivative operator are taken in the local fractional sense. Two examples have been presented showing the effectiveness of this method in solving this model on Cantor sets.
Highlights
Partial differential equations are more important than others, due to their multiple scientific uses, where they are involved in the study of some phenomena related to human life, organisms and the universe, such as engineering phenomena, mechanical phenomena, chemical phenomena and biological phenomena
The local fractional homotopy analysis method (LFHAM) method was applied successfully to local fractional biological population models and the results have been compared with integer order in [30]
The use of the LFHAM method is used to obtain the non-differentiable solution of nonlinear biological population models on Cantor sets
Summary
Partial differential equations are more important than others, due to their multiple scientific uses, where they are involved in the study of some phenomena related to human life, organisms and the universe, such as engineering phenomena, mechanical phenomena, chemical phenomena and biological phenomena. Given the importance of these equations, the knowledge of their solutions is the other more important, because it enables us to study the phenomenon associated with these equations ([9,10,11,12,13]) In this field there are many researchers interested in developing several methods that enable us to solve this kind of equations, among them, for example, are the Adomian decomposition method [14], homotopy perturbation method [15], variational iteration method [16], DJ-iteration method [17] and homotopy analysis method [18] and others.
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