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

Teaching Materials & Books

📖
Undergraduate

Statistique Inférentielle

Teaching resources

📖
first year

الوسيط في الجبر

Teaching resources

📖
Undergraduate (1st year)

الوسيط في الإحصاء و الاحتمال

Teaching resources

📖
Graduate

Fractional Calculus

Teaching resources

📖
Undergraduate (3rd year)

Functional Analysis

Teaching resources

📖
Undergraduate

Analysis I and II

Teaching resources