<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we prove that if <italic>a</italic>, <italic>b</italic> > 0 and 0 ≤ α ≤ 1, then for <italic>m</italic> = 1, 2, 3, . . . ,<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2020-0012_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mtable><mtr><mtd><mrow><msubsup><mrow><mi>r</mi></mrow><mn>0</mn><mi>m</mi></msubsup><msup><mrow><mrow><mrow><mo>(</mo><mrow><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mi>m</mi><mn>2</mn></mfrac></mrow></msup><mo>-</mo><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mi>m</mi><mn>2</mn></mfrac></mrow></msup></mrow><mo>)</mo></mrow></mrow></mrow><mn>2</mn></msup></mrow></mtd><mtd><mrow><mo>≤</mo><msubsup><mrow><mi>r</mi></mrow><mn>0</mn><mi>m</mi></msubsup><mrow><mo>(</mo><mrow><mfrac><mrow><msup><mrow><mi>b</mi></mrow><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow><mrow><mi>b</mi><mo>-</mo><mi>a</mi></mrow></mfrac><mo>-</mo><mrow><mo>(</mo><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><mi>a</mi><mi>b</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mfrac><mi>m</mi><mn>2</mn></mfrac></mrow></msup></mrow><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow></mrow></mtd><mtd><mrow><mo>≤</mo><msup><mrow><mrow><mrow><mo>(</mo><mrow><mi>α</mi><mi>a</mi><mo>+</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mi>α</mi></mrow><mo>)</mo></mrow><mi>b</mi></mrow><mo>)</mo></mrow></mrow></mrow><mi>m</mi></msup><mo>-</mo><msup><mrow><mrow><mrow><mo>(</mo><mrow><msup><mrow><mi>a</mi></mrow><mi>α</mi></msup><msup><mrow><mi>b</mi></mrow><mrow><mn>1</mn><mo>-</mo><mi>α</mi></mrow></msup></mrow><mo>)</mo></mrow></mrow></mrow><mi>m</mi></msup><mo>,</mo></mrow></mtd></mtr></mtable></mrow></math><tex-math>\matrix{ {r_0^m{{\left( {{a^{{m \over 2}}} - {b^{{m \over 2}}}} \right)}^2}} &amp; { \le r_0^m\left( {{{{b^{m + 1}} - {a^{m + 1}}} \over {b - a}} - \left( {m + 1} \right){{\left( {ab} \right)}^{{m \over 2}}}} \right)} \cr {} &amp; { \le {{\left( {\alpha a + \left( {1 - \alpha } \right)b} \right)}^m} - {{\left( {{a^\alpha }{b^{1 - \alpha }}} \right)}^m},} \cr }</tex-math></alternatives></disp-formula>where <italic>r</italic>0 = min{α, 1 – α }. This is a considerable new generalization of two refinements of the Young inequality due to Kittaneh and Manasrah, and Hirzallah and Kittaneh, which correspond to the cases <italic>m</italic> = 1 and <italic>m</italic> = 2, respectively. As applications we give some refined Young type inequalities for generalized euclidean operator radius and the numerical radius of some well-know <italic>f</italic> -connection of operators and refined some Young type inequalities for the traces, determinants, and norms of positive definite matrices.</abstract>

A new generalization of two refined Young inequalities and applications

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we combine the Riemann-Liouville integral operator and Caputo derivative to investigate a nonlinear time-singular differential equation of Lane Emden type. The considered problem involves <italic>n</italic> fractional Caputo derivatives under the conditions that neither commutativity nor semi group property is satisfied for these derivatives. We prove an existence and uniqueness analytic result by application of Banach contraction principle. Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions related to this result are established by means of the fixed point theorem of Schaefer. We end the paper by presenting to the reader some illustrative examples.</abstract>

A generalized sequential problem of Lane-Emden type via fractional calculus

<abstract xmlns="http://www.w3.org/1999/xhtml">Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert <italic>C</italic><italic>*</italic>-modules. The purpose of this paper is the introduction and the study of the concept of Controlled Continuous g-Frames in Hilbert <italic>C</italic><italic>*</italic>-Modules. Also we give some properties.</abstract>

Controlled Continuous g-Frames in Hilbert <italic>C</italic><italic>*</italic>-Modules

<abstract xmlns="http://www.w3.org/1999/xhtml">This paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the <italic>p</italic>(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on <italic>C</italic>1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve <italic>μ</italic>1(λ) and also show that, the smallest curve <italic>μ</italic>1(λ) is positive for all 0 ≤ λ &lt; <italic>C</italic><italic>H</italic>, with <italic>C</italic><italic>H</italic> is the optimal constant of Hardy type inequality.</abstract>

Laboratory LAMA Department of Mathematics Faculty of Sciences

Department of Mathematics and Statistics College of Science

Imam Mohammad Ibn Saud Islamic University (IMSIU)

AMNEA Group Department of Mathematics Faculty of Sciences and Technologies

Eigencurves of the <italic>p</italic>(·)-Biharmonic operator with a Hardy-type term

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we prove that the intermediate value theorem remains true for the conformable fractional derivative and we prove some useful results using the definition of conformable fractional derivative given in R. Khalil, M. Al Horani, A. Yousef, M. Sababhehb [4].</abstract>

On some properties of the conformable fractional derivative

<abstract xmlns="http://www.w3.org/1999/xhtml">This article deals with some existence of random solutions and Ulam stability results for a class of Caputo-Fabrizio random fractional differential equations with boundary conditions in Banach spaces. Our results are based on the fixed point theory and random operators. Two illustrative examples are presented in the last section.</abstract>

Djillali Liabes University of Sidi Bel-Abbès

Boundary Value Problem for Caputo–Fabrizio Random Fractional Differential Equations

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2020-0018_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mo>-</mo><mi>d</mi><mi>i</mi><mi>v</mi><mi> </mi><mi> </mi><mi>a</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mo>∇</mo><mi>u</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>b</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>λ</mi><mi>H</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mo>∇</mo><mi>u</mi></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math><tex-math>- div\,\,a\left( {x,u,\nabla u} \right) = b\left( x \right){\left| u \right|^{p - 2}}u + \lambda H\left( {x,u,\nabla u} \right),</tex-math></alternatives></disp-formula>where Ω is a bounded smooth domain of 𝕉<italic>N</italic>.</abstract>

Topological degree methods for a Neumann problem governed by nonlinear elliptic equation

<abstract xmlns="http://www.w3.org/1999/xhtml">In this article, we have derived some integral transforms of the polynomial weighted incomplete <italic>H</italic>-functions and incomplete ̄H-functions. The obtained image formulas are of general nature and may, as special cases, give rise to integral transforms involved with the <italic>H</italic>-functions and ̄H-functions.</abstract>

Certain integral transforms concerning the product of family of polynomials and generalized incomplete functions

<abstract xmlns="http://www.w3.org/1999/xhtml">One of the divergences between topology and ordered topology is that some topological concepts such as separation axioms and continuous maps are defined using open neighborhoods or neighborhoods without any difference, however, they are distinct on the ordered topology according to the neighborhoods: Are they open neighborhoods or not? In this paper, we present the concept of sum of the ordered spaces using pairwise disjoint topological ordered spaces and study main properties. Then, we introduce the properties of ordered additive, finitely ordered additive and countably ordered additive which associate topological ordered spaces with their sum. We prove that the properties of being <italic>T</italic><italic>i</italic>-ordered and strong <italic>T</italic><italic>i</italic>-ordered spaces are ordered additive, however, the properties of monotonically compact and ordered compact spaces are finitely ordered additive. Also, we define a mapping between two sums of the ordered spaces using mappings between the ordered spaces and deduce some results related to some types of continuity and homeomorphism. We complete this work by determining the conditions under which a topological ordered space is sum of the ordered spaces.</abstract>

Sum of the spaces on ordered setting

<abstract xmlns="http://www.w3.org/1999/xhtml">Relied on author’s first ever found multivariate Caputo fractional Taylor’s formula (2009, [1], Chapter 13), we develop and prove several multivariate left side Caputo fractional uniform Landau type inequalities.</abstract>

Multivariate Caputo left fractional Landau inequalities

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper, we show the existence of solutions of some nonlinear inequalities of the form 〈<italic>Au</italic> + <italic>g</italic>(<italic>x</italic>, <italic>u</italic>,∇ <italic>u</italic>), <italic>v −u</italic>〉 ≥〈 <italic>f</italic>, <italic>v −u〉</italic> with gradient constraint that depend on the solution itself, where <italic>A</italic> is a Leray-Lions operator defined on Orlicz spaces, <italic>g</italic> is a nonlinearity and <italic>f ∈ L</italic>1.</abstract>

Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization, we apply the Legendre-Chebyshev pseudospectral method, so that, the problem under consideration is reduced to a system of ODEs which can be solved by the second order Crank-Nicolson schema. Optimal error estimates for the semi-discrete scheme are derived in <italic>L</italic>2-norm. Numerical tests are included to demonstrate the effectiveness of the proposed method.</abstract>

Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions

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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 