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

Curriculum Vitae

Summary highlights from the academic curriculum vitae.

Download PDF
@m.benbachir@nhsm.edu.dz@mbenbachir2001@gmail.comTEL+213 663 272 051TEL+213 795 254 663ORCID0000-0003-3519-1153RGResearchGateGSGoogle ScholarYTYouTubeWOSAAZ-8207-2020

Education

2010

Ph.D. (Doctorat d'Etat) in Mathematics — USTHB, Algiers, Algeria — Thesis: Systemes lents-rapides avec problemes reduits Hamiltoniens et lequation de Cahn-Hilliard

1996

Magister in Mathematics — USTHB, Algiers, Algeria — Thesis: Problemes aux limites et Oscillations periodiques

1992

B.Sc. in Mathematics — USTHB, Algiers, Algeria

Current Position

Current

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

Research Interests

Dynamical Systems, Averaging Methods, Non-Standard Analysis, Inequalities, Singular Perturbations, Fractional Calculus, Fixed Point Theory, Fractional Differential Equations

Books

2005

Linear Algebra

Dar El Imame Malek, Blida • Arabic • Published book
2006

Probability and Statistics

OPU • Arabic • Published book

Textbooks

—

Ordinary Differential Equations

Textbook (Third-year students)
—

Course Notes on Analysis and Applications

Textbook (Second-year students)
—

Inferential Statistics

Textbook (Second-year students)
—

Topology

Textbook (Second-year students)
—

Algebra

Textbook (First-year students)
—

Elementary Statistics

Textbook (First-year students)
—

Functional analysis

Textbook (Third-year students)
—

Distributions and applications

Textbook (Fourth-year students)
—

Introduction to Fractional Calculus

Textbook (Fourth-year students)
—

Analysis I and II

Textbook (Analysis I & II)

Teaching

Undergraduate

Statistique Inférentielle

first year

الوسيط في الجبر

Undergraduate (1st year)

الوسيط في الإحصاء و الاحتمال

Graduate

Fractional Calculus

Undergraduate (3rd year)

Functional Analysis

Undergraduate

Analysis I and II

Professional Experience

1993–1995

Assistant, Department of Mathematics — University of Sciences and Technology Houari Boumediene (USTHB), Algiers, Algeria

1996–1998

Maitre Assistant, Department of Sciences — University of Sciences and Technology Saad Dahleb, Blida, Algeria

1999–2010

Maitre Assistant, Department of Sciences, Faculty of Science and Technology — University of Bechar, Bechar, Algeria

2010–2012

Associate Professor, Department of Sciences, Faculty of Science and Technology — University of Bechar, Bechar, Algeria

2012–2015

Associate Professor, Department of Mathematics and Computer Science, Faculty of Science and Technology — University of Khemis-Miliana, Ain Defla, Algeria

2015–2019

Professor, Department of Mathematics and Computer Science, Faculty of Science and Technology — University of Khemis-Miliana, Ain Defla, Algeria

2019–2022

Professor, Department of Mathematics, Faculty of Sciences — Saad Dahlab University, Blida, Algeria — Until Aug 2022

2022–Present

Professor — National Higher School of Mathematics, Sidi Abdellah (Algiers), Algeria — Since Sep 2022, P.O. Box 75, Mahelma 16093