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

Prof. Maamar Benbachir

Professor of Mathematics — National Higher School of Mathematics, Sidi Abdellah (Algiers), Algeria
Sidi Abdellah, Algiers, Algeria

•Sidi Abdellah, Algiers, Algeria
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Professor Maamar Benbachir is a mathematician. He graduated from the University of Sciences and Technology Houari Boumediene (USTHB) in Algiers, where he earned both a “Magister” and a PhD in mathematics, in 1996 and 2010, respectively.

Professor Benbachir’s career includes teaching positions at several universities in Algeria. He began his academic journey at Bechar University (1997-2012), followed by Khemis Miliana University (2012-2019), and then Blida University (2019-2021). He is currently at the National Higher School of Mathematics. He has been a professor since 2015.

From 2017 to 2020, he served as the President of the National Council of Mathematics and Computer Science Pedagogical Domain, contributing significantly to the advancement of mathematics education in Algeria.

His primary research interests lie in fractional differential equations and fixed-point theory, areas in which he has made notable contributions to the field.

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