On solutions of fractal fractional differential equations
Abdon Atangana, Ali Akgül
Abstract
<p style='text-indent:20px;'>New class of differential and integral operators with fractional order and fractal dimension have been introduced very recently and gave birth to new class of differential and integral equations. In this paper, we derive exact solution of some important ordinary differential equations where the differential operators are the fractal-fractional. We presented a new numerical scheme to obtain solution in the nonlinear case. We presented the numerical simulation for different values of fractional orders and fractal dimension.
Topics & Concepts
MathematicsFractalMathematical analysisNonlinear systemFractional calculusFractal dimensionClass (philosophy)Differential equationOrdinary differential equationFractal derivativeDimension (graph theory)Applied mathematicsPure mathematicsFractal analysisPhysicsComputer scienceArtificial intelligenceQuantum mechanicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsMathematical functions and polynomials