Existence and stability for a nonlinear hybrid differential equation of fractional order via regular Mittag–Leffler kernel

2021 ◽  
Author(s):  
Ibrahim Slimane ◽  
Zoubir Dahmani ◽  
Juan J. Nieto ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Existence And Stability ◽  
Hybrid Differential Equation ◽  
Nonlinear Hybrid

scholarly journals Boundary Value Problem of Nonlinear Hybrid Differential Equations with Linear and Nonlinear Perturbations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Said Melliani ◽  
Abdelati El Allaoui ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
Nonlinear Perturbations ◽  
Banach’S Fixed Point Theorem ◽  
Linear And Nonlinear ◽  
Hybrid Differential Equation ◽  
Hybrid Differential Equations ◽  
Nonlinear Hybrid

The aim of this paper is to study a boundary value problem of the hybrid differential equation with linear and nonlinear perturbations. It generalizes the existing problem of second type. The existence result is constructed using the Leray–Schauder alternative, and the uniqueness is guaranteed by Banach’s fixed-point theorem. Towards the end of this paper, an example is provided to illustrate the obtained results.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

scholarly journals Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang Liu ◽  
Zhang Weiguo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Boundary Value ◽  
Order Derivative ◽  
Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

scholarly journals Fractional-Order Logistic Differential Equation with Mittag–Leffler-Type Kernel

2021 ◽  
Vol 5 (4) ◽  
pp. 273
Author(s):  
Iván Area ◽  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Differential Equations ◽  
Formal Power Series ◽  
Fractional Order ◽  
Numerical Approximations ◽  
Formal Power

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series. Some numerical approximations are implemented by using truncated series.

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