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The minimax approach for a class of variable order fractional differential equation
Author(s) -
Semary Mourad S.,
Hassan Hany N.,
Radwan Ahmed G.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5545
Subject(s) - mathematics , minimax , variable (mathematics) , order (exchange) , chebyshev filter , fractional calculus , nonlinear system , differential equation , function (biology) , class (philosophy) , mathematical analysis , mathematical optimization , computer science , physics , finance , quantum mechanics , evolutionary biology , economics , biology , artificial intelligence
This paper introduces an approximate solution for Liouville‐Caputo variable order fractional differential equations with order 0 < α ( t ) ≤ 1 . The solution is adapted using a family of fractional‐order Chebyshev functions with unknown coefficients. These coefficients have been obtained by using an optimization approach based on minimax technique and the least p th optimization function. Several linear and nonlinear fractional‐order differential equations are discussed using the proposed technique for fixed and variable order fractional‐order derivatives. Moreover, the response of RC charging circuit with variable order fractional capacitor is studied for different cases. Several comparisons with related published techniques have been added to illustrate the accuracy of the proposed approach.