Existence and stability of solution for nonlinear differential equations with ψ−Hilfer fractional derivative

2021 ◽  
pp. 107457
Author(s):  
Jue-liang Zhou ◽  
Shu-qin Zhang ◽  
Yu-bo He
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Nonlinear Differential Equations ◽  
Hilfer Fractional Derivative ◽  
Stability Of Solution ◽  
Existence And Stability

Numerical and analytical solutions of nonlinear differential equations involving fractional operators with power and Mittag-Leffler kernel

2018 ◽  
Vol 13 (1) ◽  
pp. 13 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J.F. Gómez-Aguilar
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Nonlinear Differential Equations ◽  
Fractional Operators ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractional Differential ◽  
Derivative Order

Analytical and numerical simulations of nonlinear fractional differential equations are obtained with the application of the homotopy perturbation transform method and the fractional Adams-Bashforth-Moulton method. Fractional derivatives with non singular Mittag-Leffler function in Liouville-Caputo sense and the fractional derivative of Liouville-Caputo type are considered. Some examples have been presented in order to compare the results obtained, classical behaviors are recovered when the derivative order is 1.

Homotopy Analysis Method for Nonlinear Differential Equations with Fractional Orders

2008 ◽  
Vol 63 (5-6) ◽  
pp. 241-247 ◽  
Author(s):  
Yin-Ping Liu ◽  
Zhi-Bin Li
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Nonlinear Differential Equations ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Fractional Orders

The aim of this paper is to solve nonlinear differential equations with fractional derivatives by the homotopy analysis method. The fractional derivative is described in Caputo’s sense. It shows that the homotopy analysis method not only is efficient for classical differential equations, but also is a powerful tool for dealing with nonlinear differential equations with fractional derivatives.

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