<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mjpaa_2017.3.1.2.jpg"></inline-graphic>. By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mjpaa_2017.3.1.3.jpg"></inline-graphic>. The space FṄsp,λ,q(ℝ3) covers the classical spaces Ḃsq and FḂsp,q(ℝ3) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].</abstract>

Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we establish Hermite-Hadamard type inequalities for (α, m)-convex functions via fractional integrals.</abstract>

Hermite-Hadamard Type Inequalities for (α, m)- Convex Functions via Fractional Integrals

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms. We give some Hermite-Hadamard type inequalities for convex, harmonically convex and p-convex functions. Some results presented in this paper for p-convex functions, provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.</abstract>

Hermite-Hadamard type inequalities for p-convex functions via fractional integrals

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results by using modified version of contraction principle. Further, our prime aim is to present various Ulam-Hyers stability and Eα-Ulam-Hyers stability results via successive approximation method. </abstract>

Stability via successive approximation for nonlinear implicit fractional differential equations

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this research we aim to explore some properties of m-convex functions from the point of view of functional equations or better, functional inequalities. So far studies of m- convexity have been devoted mainly to establish properties, inequalities and examples on the topic, but not to look at the problem from the perspective of functional inequalities.</abstract>

m-Convexity and Functional Equations

<abstract xmlns="http://www.w3.org/1999/xhtml"> By using the generalized Hölder’s and Minkowski’s integral inequalities, some inequalities for the m-th derivative of the (q; k)-Gamma function are established. Consequently, some previous results are recovered as particular cases of the present results. </abstract>

Inequalities for the m-th derivative of the (q; k)-Gamma function

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we prove the existence of in finitely many solutions for the following system <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mjpaa.2017.3.1.1.jpg"></inline-graphic> by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle and the theory of the anisotropic variable exponent Sobolev spaces 2010 Mathematics Subject Classification. 35K05 - 35K55. </abstract>

Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml"> Some new inequalities of Hermite-Hadamard type for HA-convex functions defined on positive intervals are given.</abstract>

Inequalities of Hermite-Hadamard Type for HA-Convex Functions

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, the notion of generalized (s; m; ξ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized (s; m; ξ)-preinvex functions along with beta function are given. Moreover, we establish some new Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions via classical and Riemann-Liouville fractional integrals. These results not only extend the results appeared in the literature (see [10],[11]), but also provide new estimates on these types. At the end, some conclusions are given.</abstract>

Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/8262_1.jpg"></inline-graphic>where is a bounded domain, the function a can be a singular potential, g is a suitable function which will be specified later and p, θ Abstract. In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem under natural conditions on the data. The question of global existence is also analyzed.</abstract>

Fractional parabolic problems with a nonlocal initial condition

AHEAD OF PRINT

Volume 9 (2023): Issue 3 (September 2023)

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Volume 2 (2016): Issue 2 (December 2016)

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Volume 1 (2015): Issue 2 (December 2015)

Volume 1 (2015): Issue 1 (June 2015)

Moroccan Journal of Pure and Applied Analysis

 The Moroccan Journal of Pure and Applied Analysis "MJPAA" (Print ISSN: 2605-6364) is a peer-reviewed open access journal published by the "Université Sidi Mohamed Ben Abdellah" (Sidi Mohamed Ben Abdallah University), covering all main-stream branches of pure and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, numerical analysis, optimization theory, and control theory.   MJPAA is published by Sidi Mohamed Ben Abdallah University in three issues in January, May and September.   Why subscribe and read    The journal covers a wide range of branches of mathematical analysis.   Pure and applied analysis topics are intensely studied by researchers throughout the world especially in Africa, the Arab and European countries.   An edition committee of high-level and international renown.   Editorial board representing different regions of the world and various research teams.      Why submit    No publication charges for the authors or their institutions.   The journal is available to be indexed in the most important databases.   The journal is among the best in its field in Africa and the Arab world.      Rejection Rate    45%      Archiving   Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.   Plagiarism Policy   The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.   Publisher:Sidi Mohamed Ben Abdallah University (Route Imouzzer, BP 2626 Fez 30000, Morocco, Tel. : 0212 5 35 60 96 60/ 61)   Contact:Professor Youssef Akdim, Sidi Mohamed Ben Abdellah Universitymjpaa.edition1@usmba.ac.ma 