Entropy · 2017 · 90 citations · 43 references
Natural SciencesMathematicsOncologyDifferential EquationsDynamical SystemsStochastic ProcessesBifurcation TheoryChaos TheoryLaplace Transform MethodsNonlinear DynamicsNumerical Methods For Differential EquationsStability TheoryAttractorsChaos In Biological SystemsChaotic AttractorsChaotic DynamicsExponential DecayExponential Decay ModelsFractional Differential EquationsLaplace Transform
In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.
43
A new Definition of Fractional Derivative without Singular Kernel
Michèle Caputo, Mauro Fabrizio · 2015 · 2.4K citations