Open AccessSemi-analytic solutions of nonlinear multidimensional fractional differential equations
Author(s) -
Monica Botros,
E. A. A. Ziada,
I. L. ElKalla
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022623
Subject(s) - mathematics , fractional calculus , adomian decomposition method , convergence (economics) , nonlinear system , convolution (computer science) , decomposition method (queueing theory) , kernel (algebra) , mathematical analysis , derivative (finance) , exact solutions in general relativity , series (stratigraphy) , type (biology) , differential equation , pure mathematics , paleontology , ecology , physics , discrete mathematics , quantum mechanics , machine learning , artificial neural network , computer science , financial economics , economics , biology , economic growth
In this paper, the Adomian decomposition method (ADM) and Picard technique are used to solve a class of nonlinear multidimensional fractional differential equations with Caputo-Fabrizio fractional derivative. The main advantage of the Caputo-Fabrizio fractional derivative appears in its non-singular kernel of a convolution type. The sufficient condition that guarantees a unique solution is obtained, the convergence of the series solution is discussed, and the maximum absolute error is estimated. Several numerical problems with an unknown exact solution are solved using the two techniques. A comparative study between the two solutions is presented. A comparative study shows that the time consumed by ADM is much smaller compared with the Picard technique.