Number of posts

(Google Scholar)

Number of quotes

Google Scholar)

H-index (Google

Scholar)

Complete list of team members by rank starting with the highest rank

Last name First Name

Attachment structure

Se xed

Date of Birth

Last Diploma

Grade

Specialty

Google Account Schto smell

Number Of Publications

Number Of Quotes (Google

Scholar)

H-index (Google Scholar)

Benbachir Maamar

Univ. Blida1

M

26/10/1967

Ph.D

Prof.

Analysis

https://Scholar.Google.Com

/Quotes?User=Gjcgvy4aaa aj

32

117

6

Chaouchi Belkacem

Univ. K. Miliana

M

20/02/1976

Doctorate

MCB

Analysis

https://Scholar.Google.Com

/Quotes?User=Kyshrrcaaa aj&Hl=Fr&Oi=Sra

8

14

2

Univ. Blida 1

M

02/06/1965

Master

MAA

Analysis

02

Benaissa Lakhdar

University of Algiers1

M

25/04/1975

Master

MAA

Analysis

https://scholar.google.fr/citat ions?user=2YMbrAcAAAA

J&hl=fr&oi=ao

4

4

1

NB: Applicant members must not, under any circumstances, belong to an already approved laboratory.

Description of the objectives, missions and activities of the team

(It must necessarily fit with the themes of the laboratory)

Overall goals (Describe in about ten lines the objective of the research carried out by the team)

From equations resulting from mechanics and physics, in general partial differential equations of the elliptical or parabolic type, we set ourselves the goal of developing and implementing a qualitative and quantitative study for this type of problem. . The study of these problems uses several tools of functional analysis. The abstract point of view adopted is essentially based on operator theory. Tools used include fractional calculus, singular perturbation methods, functional interpolation theory, and semigroups of linear operators.

As a second phase, we focus on the numerical approach. The implication of numerical methods such as finite differences, finite elements, finite volume, will aim to validate the theoretical results obtained previously.

Equations with derivatives of fractional order generalize equations with derivatives of integer order. The fractional approach appears today as a promising way to better describe real phenomena from finance, solid-state physics, signal processing, quantum mechanics, porous media and many other fields. The development of fractional analysis itself represents a growing branch of mathematics. In this work, we propose to study some problems with boundary conditions and derivatives of fractional order. The aim is to provide sufficient conditions guaranteeing the existence of solutions and

positive solutions and uniqueness of solutions. Our main tool will be the different techniques provided by the

fixed point theory.

Scientific Foundations (Define the major work themes that the team proposes)

Study of certain partial differential equations in non-regular domains. Study of the non-linear problems ODE and PDE by the method of the topological degree of Leray-Schauder. Studies of certain fractional differential equations by fixed point techniques.

Studies of the stability of differential equations with integer and fractional derivatives.

Keywords: Non-linear ODE and PDE, Leray-Schauder Topological degree, mathematical modelling, mechanics of

continuums, operational calculus of Dunford, the theory of semigroups of linear operators, numerical approximations, domains with cusps, polygonal domains, fractional derivative, derivative of Riemann-Liouville, derivative of Caputo, derivative of Marchaud, derivative of Grünwald-Letnikov, Green's fractional function, fixed point, existence of solution, positive solution.