MB
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
M. Benbachir

Research Interests

01

Dynamical Systems

02

Averaging Methods

03

Non-Standard Analysis

04

Inequalities

05

Singular Perturbations

06

Fractional Calculus

07

Fixed Point Theory

08

Fractional Differential Equations

Keywords

Dynamical SystemsAveraging MethodsNon-Standard AnalysisInequalitiesSingular PerturbationsFractional CalculusFixed Point TheoryFractional Differential Equations