rss_2.0Annals of West University of Timisoara - Mathematics and Computer Science FeedSciendo RSS Feed for Annals of West University of Timisoara - Mathematics and Computer Sciencehttps://sciendo.com/journal/AWUTMhttps://www.sciendo.comAnnals of West University of Timisoara - Mathematics and Computer Science Feedhttps://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470cf8871e4585e08aa614c/cover-image.jpghttps://sciendo.com/journal/AWUTM140216Existence and Successive Approximations of Mild Solution for Integro-differential Equations in Banach Spaceshttps://sciendo.com/article/10.2478/awutm-2024-0003<abstract> <title style='display:none'>Abstract</title> <p>This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00032024-03-02T00:00:00.000+00:00On the Ψ − Conditional Asymptotic Stability of a Nonlinear Lyapunov Matrix Differential Equation with Integral Term as Right Sidehttps://sciendo.com/article/10.2478/awutm-2024-0002<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to give sufficient conditions for Ψ − conditional asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00022024-03-02T00:00:00.000+00:00A Study of Computational Genome Assembly by Graph Theoryhttps://sciendo.com/article/10.2478/awutm-2024-0001<abstract> <title style='display:none'>Abstract</title> <p>The assembly of billions of short sequencing reads into a contiguous genome is a daunting task. The foundation knowledge of current DNA assembly models is concentrated among a select group, where the solution to the genome assembly challenge lies in proper ordering the genomic data. This contribution’s objective is to provide an overview of the original graph models used in DNA sequencing by hybridization. With the updated analytical approach based on the bidirectional bipartite graph class, the theoretical basic structure of the DNA assembly model has been described in new perspective by incorporating few short hypothetical DNA sequences. On the Galaxy platform, by using Spades assembler and Velvet assembler, the comparative outcomes of an experiment are presented, and we also identify their working schemes. Here, the working principle of de Bruijn graph has been discussed in broader point of view.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00012024-02-24T00:00:00.000+00:00Non-convex perturbation to evolution problems involving Moreau’s sweeping processhttps://sciendo.com/article/10.2478/awutm-2023-0012<abstract> <title style='display:none'>Abstract</title> <p>Along this paper, we study an evolution inclusion governed by the so-called sweeping process. The right side of the inclusion contains a set-valued perturbation, supposed to be the external forces exercised on the system. We prove existence and relaxation results under weak assumptions on the perturbation by taking a truncated Lipschitz condition. These perturbations have non-convex and unbounded values without any compactness condition; we just assume a linear growth assumption on the element of minimal norm. The approach is based on the construction of approximate solutions. The relaxation is obtained by proving the density of the solution set of the original problem in a closure of the solution set of the relaxed one.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00122023-12-01T00:00:00.000+00:00Fixed Point Results in Incomplete Metric and Dislocated Metric Spaceshttps://sciendo.com/article/10.2478/awutm-2023-0011<abstract> <title style='display:none'>Abstract</title> <p>This paper deals with the existence and uniqueness of common fixed points in metric and dislocated metric spaces. In addition, an application and some illustrative examples are given in order to justify the validity and credibility of our results, also, their superiority over some similar theorems existing in unique common fixed points theory’s domain.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00112023-09-21T00:00:00.000+00:00Stability properties of a Cournot-type oligopoly model with time delayhttps://sciendo.com/article/10.2478/awutm-2023-0010<abstract> <title style='display:none'>Abstract</title> <p>The paper studies a Cournot game involving <italic>n</italic> private firms, where the firms’ interactions are analyzed in a discrete-time setting with time delay. The past production levels of other private firms have an impact on the production levels of each private firm. We performed a local stability analysis on the nonlinear system associated with the model and found that it has only one equilibrium point, which is asymptotically stable if and only if some conditions involving the number of firms, the degree of product di erentiation and the time delay are fulfilled. In addition, numerical examples are presented in this paper, which illustrate the theoretical results obtained.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00102023-09-21T00:00:00.000+00:00Estimate of third Hankel determinant for a subfamily of analytic functionshttps://sciendo.com/article/10.2478/awutm-2023-0009<abstract> <title style='display:none'>Abstract</title> <p>In this article, our aim is to study analytic functions related with Salagean operator and associated with the right half of the lemniscate of Bernoulli. We find the estimates of the third Hankel determinant for new family of analytic functions. It is important to mention that our results generalize a number of existence results in the literature.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00092023-07-31T00:00:00.000+00:00On uniform dichotomy in mean of stochastic skew-evolution semiflows in Banach spaceshttps://sciendo.com/article/10.2478/awutm-2023-0008<abstract> <title style='display:none'>Abstract</title> <p>In this paper we consider three concepts of uniform dichotomy in mean for stochastic skew-evolution semiflows: uniform exponential dichotomy in mean, uniform polynomial dichotomy in mean and uniform <italic>h</italic>- dichotomy in mean. Some characterizations of these notions and connections between these concepts are given. The obtained results can be considered generalizations to the dichotomy case of the results from [29].</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00082023-07-31T00:00:00.000+00:00Entropy- A Tale of Ice and Firehttps://sciendo.com/article/10.2478/awutm-2023-0002<abstract> <title style='display:none'>Abstract</title> <p>In this review paper, we recall, in a unifying manner, our recent results concerning the Lie symmetries of nonlinear Fokker-Plank equations, associated to the (weighted) Tsallis and Kaniadakis entropies. The special values of the Tsallis parameters, highlighted by the classification of these symmetries, clearly indicate algebraic and geometric invariants which differentiate the Lie algebras involved. We compare these values with the ones previously obtained by several authors, and we try to establish connections between our theoretical families of entropies and specific entropies arising in several applications found in the literature.</p> <p>We focus on the discovered correlations, but we do not neglect dissimilarities, which might provide -in the future-deeper details for an improved extended panorama of the Tsallis entropies.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00022023-05-03T00:00:00.000+00:00Prefacehttps://sciendo.com/article/10.2478/awutm-2023-0001ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00012023-05-03T00:00:00.000+00:00Determinant Inequalities for Positive Definite Matrices Via Diananda’s Result for Arithmetic and Geometric Weighted Meanshttps://sciendo.com/article/10.2478/awutm-2023-0003<abstract> <title style='display:none'>Abstract</title> <p>In this paper we prove among others that, if (<italic>A<sub>j</sub></italic>)<sub><italic>j</italic>=1,...,<italic>m</italic></sub> are positive definite matrices of order <italic>n</italic> ≥ 2 and <italic>q<sub>j</sub></italic> ≥ 0, <italic>j</italic> = 1, ..., <italic>m</italic> with <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2023-0003_eq_001.png"/><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="M1"><mml:mstyle displaystyle="true"><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math>$$\sum\nolimits_{j = 1}^m {{q_j} = 1} $$</tex-math></alternatives></inline-formula>, then <disp-formula id="j_awutm-2023-0003_eq_002"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2023-0003_eq_002.png"/><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" id="M2"><mml:mtable columnalign="left"><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mn>0</mml:mn></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mo>≤</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>min</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>∈</mml:mo><mml:mo>{</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:msub><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow> <mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mo>×</mml:mo></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:munderover><mml:mrow><mml:msup><mml:mo>∑</mml:mo><mml:mtext>​</mml:mtext></mml:msup></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:mi>det</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> 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<mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow> <mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mo>≤</mml:mo></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:munderover><mml:mrow><mml:msup><mml:mo>∑</mml:mo><mml:mtext>​</mml:mtext></mml:msup></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:mi>det</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:mi>det</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:munderover><mml:mrow><mml:msup><mml:mo>∑</mml:mo><mml:mtext>​</mml:mtext></mml:msup></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mo>≤</mml:mo></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mrow><mml:mi>min</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>∈</mml:mo><mml:mo>{</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:msub><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow> <mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mo>×</mml:mo></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:munderover><mml:mrow><mml:msup><mml:mo>∑</mml:mo><mml:mtext>​</mml:mtext></mml:msup></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:mi>det</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:munder><mml:mrow><mml:msup><mml:mo>∑</mml:mo><mml:mtext>​</mml:mtext></mml:msup></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>i</mml:mi><mml:mo>&lt;</mml:mo><mml:mi>j</mml:mi><mml:mo>≤</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>q</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:mi>det</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow> <mml:mo>]</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math> <tex-math><?CDATA \begin{eqnarray}0 &#x0026; \le \frac{1}{1-{\min }_{i\in \{1,\ldots ,m\}}\{{q}_{i}\}}\\ \times &#x0026; [\underset{i=1}{\overset{m}{{\sum }^{\text{}}}}{q}_{i}(1-{q}_{i}){[\det ({A}_{i})]}^{-1}-{2}^{n+1}\mathop{{\sum }^{\text{}}}\limits_{1\le i\lt j\le m}{q}_{i}{q}_{j}{[\det ({A}_{i}+{A}_{j})]}^{-1}]\\ \le &#x0026; \underset{i=1}{\overset{m}{{\sum }^{\text{}}}}{q}_{i}{[\det ({A}_{i})]}^{-1}-{[\det (\underset{i=1}{\overset{m}{{\sum }^{\text{}}}}{q}_{i}{A}_{i})]}^{-1}\\ \le &#x0026; \frac{1}{{\min }_{i\in \{1,\ldots ,m\}}\{{q}_{i}\}}\\ \times &#x0026; [\underset{i=1}{\overset{m}{{\sum }^{\text{}}}}{q}_{i}(1-{q}_{i}){[\det ({A}_{i})]}^{-1}-{2}^{n+1}\mathop{{\sum }^{\text{}}}\limits_{1\le i\lt j\le m}{q}_{i}{q}_{j}{[\det ({A}_{i}+{A}_{j})]}^{-1}].\end{eqnarray}?></tex-math></alternatives></disp-formula></p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00032023-05-03T00:00:00.000+00:00Uniqueness Results for Fractional Integro-differential Equations with State-Dependent Nonlocal Conditions in Fréchet Spaceshttps://sciendo.com/article/10.2478/awutm-2023-0004<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to study the existence of the unique mild solution for non-linear fractional integro-differential equations with state-dependent nonlocal condition. The result was obtained by using nonlinear alternative of Granas-Frigon for contraction in Fréchet spaces. To illustrate the result, an example is provided.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00042023-05-03T00:00:00.000+00:00Hyperbolic Tangent Like Relied Banach Space Valued Neural Network Multivariate Approximationshttps://sciendo.com/article/10.2478/awutm-2023-0005<abstract> <title style='display:none'>Abstract</title> <p>Here we examine the multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ<sup><italic>N</italic></sup> , <italic>N</italic> ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a hyperbolic tangent like sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00052023-05-03T00:00:00.000+00:00Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equationshttps://sciendo.com/article/10.2478/awutm-2023-0007<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we study the following fractional differential equation involving the Atangana-Baleanu-Caputo fractional derivative: <disp-formula id="j_awutm-2023-0007_eq_001"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2023-0007_eq_001.png"/><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" id="M1"><mml:mrow><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:mtable columnalign="left"><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:mi>A</mml:mi><mml:mi>B</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:msubsup><mml:mi>D</mml:mi><mml:mi>τ</mml:mi><mml:mi>θ</mml:mi></mml:msubsup><mml:mo stretchy="false">[</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϑ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϑ</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϑ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">]</mml:mo><mml:mo>=</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϑ</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϑ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>ϑ</mml:mi><mml:mo>∈</mml:mo><mml:mi>J</mml:mi><mml:mo>:</mml:mo><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo stretchy="false">]</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:mi>x</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>a</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>φ</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:mi>ℝ</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow> </mml:mrow></mml:mrow></mml:math><tex-math>$$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ) - F(\vartheta ,x(\vartheta ))] = G(\vartheta ,x(\vartheta )),\;\;\;{\kern 1pt} \vartheta \in J: = [a,b],} \hfill \cr {x(a) = {\varphi _a} \in .} \hfill \cr } } \right.$$</tex-math></alternatives></disp-formula></p> <p>The result is based on a Dhage fixed point theorem. Further, an example is provided for the justification of our main result.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00072023-05-03T00:00:00.000+00:00Piecewise Polynomial Least Squares Method for Differential Equations of Fractional Orderhttps://sciendo.com/article/10.2478/awutm-2023-0006<abstract> <title style='display:none'>Abstract</title> <p>In this paper a new method to compute approximate analytical solutions for differential equations of fractional order is presented. The proposed computational method, called the Piecewise Polynomial Least Squares Method (PWPLSM), is a combination of the Polynomial Least Squares Method and of piecewise-defined functions. Numerical results for differential equations of different fractional orders are discussed. The approximate solutions obtained with PWPLSM are compared with other existing analytical and numerical solutions. The tables and figures included demonstrate the accuracy of the new method.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00062023-05-03T00:00:00.000+00:00Fuzzy quasi-b-metric spaceshttps://sciendo.com/article/10.2478/awutm-2022-0015<abstract> <title style='display:none'>Abstract</title> <p>In this paper we present a new approach for the fuzzy quasi-b-metric spaces and we obtain some properties of these spaces. A special attention is granted to the decomposition theorems of a fuzzy quasi-b-metric into a right continuous and ascending family of quasi-b-metrics. Finally, some future lines of research are highlighted.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2022-00152022-12-24T00:00:00.000+00:00On uniform logarithmic dichotomy of discrete skew-evolution semiflowshttps://sciendo.com/article/10.2478/awutm-2022-0016<abstract> <title style='display:none'>Abstract</title> <p>The paper considers two notions of logarithmic dichotomy for discrete skew-evolution semiflows in Banach spaces. We establish the relation between them, we give a characterization for the uniform logarithmic dichotomy of Zabczyk type and a sufficient criteria for the uniform logarithmic dichotomy.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2022-00162022-12-24T00:00:00.000+00:00On some growth concepts for dichotomic behaviors of evolution operatorshttps://sciendo.com/article/10.2478/awutm-2022-0017<abstract> <title style='display:none'>Abstract</title> <p>The aim of the present paper is to emphasize some growth concepts for the dichotomic behavior of evolution operators in Banach spaces. In fact, we approach the exponential growth, the polynomial growth and the <italic>h</italic>-growthfor both uniform and nonuniform cases. Connections between concepts are established. Majorization criteria for the uniform behaviors are given.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2022-00172022-12-24T00:00:00.000+00:00A sufficient condition for local controllability of a Caputo type fractional differential inclusionhttps://sciendo.com/article/10.2478/awutm-2022-0013<abstract> <title style='display:none'>Abstract</title> <p>We consider a Cauchy problem for a fractional differential inclusion defined by a Caputo type fractional derivative and we obtain a sufficient condition for local controllability along a reference trajectory in terms of a certain fractional variational differential inclusion associated to the initial problem.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2022-00132022-12-24T00:00:00.000+00:00The Ψ–Asymptotic Equivalence of the Lyapunov Matrix Differential Equations with Integral Term as Right Side and Modified Argumenthttps://sciendo.com/article/10.2478/awutm-2022-0018<abstract> <title style='display:none'>Abstract</title> <p>Using the notion of strict h-contraction, existence results for Ψ-asymptotic equivalence of two pairs of (Lyapunov) matrix differential equations with integral term as right side and modified argument are given.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2022-00182022-12-24T00:00:00.000+00:00en-us-1