{"title":"Generalized Hermite polynomial sequences generated by integral powers of a first order differential–difference Dunkl operator","authors":"Mohamed Khalfallah","doi":"10.1007/s11565-026-00719-z","DOIUrl":"10.1007/s11565-026-00719-z","url":null,"abstract":"<div><p>This paper is dedicated to the investigation of polynomial sequences, which are not necessarily orthogonal, generated by integral composite powers of a first order differential–difference Dunkl operator and intimately linked to the Dunkl-classical polynomials. This link is established through the canonical element of their dual sequences. For those sequences that satisfy orthogonality, the resulting polynomials coincide with the generalized Hermite polynomials. Additionally, we derive new Rodrigues-type formulas for the generalized Hermite polynomials.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Octonion-Valued probability theory using the right-sided octonion fourier transform","authors":"N. Safouane, A. Achak, R. El Azar","doi":"10.1007/s11565-026-00714-4","DOIUrl":"10.1007/s11565-026-00714-4","url":null,"abstract":"<div><p>This paper introduces a novel framework for octonion-valued probability theory based on the right-sided three-dimensional octonion Fourier transform (OFT). We define the octonion probability density function and the associated octonion characteristic function, and establish their fundamental properties including uniform continuity, boundedness, and inversion formulas. Using the right-sided OFT, we derive expressions for expected values, moments, and covariances that explicitly account for the non-commutativity and non-associativity of octonion multiplication. Component-wise decompositions of the characteristic function are obtained using parity arguments, and translation covariance properties are established. Several examples illustrate the differences between classical, quaternion, and octonion probability theories. This work lays the foundation for higher-dimensional probability models within Cayley-Dickson algebras and opens new directions for applications in three-dimensional signal processing.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Well-posedness and decay for a (upvarphi )-caputo time-fractional superdiffusion equation in Lorentz spaces","authors":"Brahim Benaissi, Yacine Arioua","doi":"10.1007/s11565-026-00720-6","DOIUrl":"10.1007/s11565-026-00720-6","url":null,"abstract":"<div><p>We study a time-fractional superdiffusion equation involving a <span>(upvarphi )</span>-Caputo derivative and a fractional Laplacian within a Lorentz-space framework. First, we analyze the associated linear problem. By combining the Fourier transform in space with the <span>(upvarphi )</span>-Laplace transform in time, we derive explicit representation formulas for the Green kernels. These kernels are expressed in terms of Fox <span>(H)</span>-functions, which allow us to obtain sharp pointwise bounds and decay estimates in Lorentz spaces. We then consider the corresponding semilinear equation with a singular source term. Using the linear estimates, we establish local well-posedness of mild solutions in weighted Lorentz spaces, together with continuous dependence on the initial data and a blow-up alternative. Finally, we discuss the scaling structure induced by the decay estimates and identify <span>( p_c(uprho )=1+frac{2updelta ,uprho }{upalpha d} )</span> as a natural candidate critical exponent in this setting.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comparative numerical study of caputo time-fractional reaction–diffusion equations with applications in physical phenomena","authors":"Ahmed Hassan","doi":"10.1007/s11565-026-00706-4","DOIUrl":"10.1007/s11565-026-00706-4","url":null,"abstract":"<div><p>This paper presents numerical solutions for linear and nonlinear fractional partial differential equations (Cauchy reaction diffusion) applying an approximation method called the Least Square Residual Power Series Method (LSRPSM). In addition to presenting the fractional Wronskian definition, the Caputo sense has been used to evaluate the fractional order derivative operator. The Least Squares Method (LSM) and the Residual Power Series Method (RPSM) are combined in this flexible technique. Consequently, we produced a rapidly convergent series with clearly defined elements for the time fractional Cauchy Reaction Diffusion Equations (CRDEs). Compared to exact solutions, RPSM and Elzaki residual power series method (ERPSM). The LSRPSM provides sufficient accuracy when applied to approximation solutions. The numerical solutions to fractional partial differential equations and their graphical representations will be covered in our final section. We are charting the outcomes of each of the partial fraction differential equations to show that MATLAB produces superior results.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. B. Gajera, R. K. Jana, N. A. Khan, A. K. Shukla
{"title":"Extended q-Jacobi polynomial and its properties","authors":"S. B. Gajera, R. K. Jana, N. A. Khan, A. K. Shukla","doi":"10.1007/s11565-026-00713-5","DOIUrl":"10.1007/s11565-026-00713-5","url":null,"abstract":"<div><p>In this paper, we define an extended <span>( textit{q} )</span>-Jacobi polynomial using the Wright-type <span>( textit{q} )</span>-hypergeometric function and discuss its analytical properties, including recurrence and contiguous relations, integral and derivative formulas, as well as integral representations. Also, integral transforms, such as the Laplace, Sumudu, and Natural transforms have been derived.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pointwise orbital proximal contractions and best proximity results in hyperconvex metric spaces","authors":"Moosa Gabeleh, Jack Markin","doi":"10.1007/s11565-026-00707-3","DOIUrl":"10.1007/s11565-026-00707-3","url":null,"abstract":"<div><p>We introduce new classes of pointwise orbital contractions for mappings defined on pairs of subsets of metric spaces and investigate their best proximity properties in hyperconvex metric spaces. First, we define the notion of a pointwise orbital cyclic contraction and establish the existence of best proximity points for such mappings acting on admissible pairs of subsets of a hyperconvex metric space. As a consequence, a novel fixed point theorem is obtained for pointwise orbital contractions defined on a single admissible subset. We then study the noncyclic case by introducing pointwise orbital noncyclic contractions. Using minimal admissible invariant pairs and the concept of semi-sharp proximinality, we prove the existence of best proximity pairs for distance-preserving noncyclic mappings in hyperconvex setting. Furthermore, we show that in Banach spaces the semi-sharp proximinality of every convex pair characterizes strict convexity. Finally, motivated by asymptotic contraction techniques, we introduce the class of asymptotic proximal pointwise cyclic contractions and prove a best proximity point theorem under a suitable geometric notion, called property UC, for admissible pairs.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Snehashree, C Siddabasappa, B. Patil Mallikarjun
{"title":"A numerical study on mixed convective Newtonian nanofluid flow through a porous channel: Local thermal non-equilibrium approach","authors":"R. Snehashree, C Siddabasappa, B. Patil Mallikarjun","doi":"10.1007/s11565-026-00708-2","DOIUrl":"10.1007/s11565-026-00708-2","url":null,"abstract":"<div><p>This paper presents a numerical investigation of the influences of local thermal non-equilibrium (LTNE) and non-uniform heat source/sink on the convective flow of a Newtonian nanofluid through a vertical porous channel, using the shooting method. The analysis incorporates the Oberbeck-Boussinesq approximation, as well as the thermophoresis effect and Brownian motion effect, to capture the significant influence of nanofluids on flow dynamics and heat transfer characteristics. Plots and tables are used to analyze the impact of flow parameters on the heat transfer and mass transfer characteristics of the individual phases. The study focuses on clarifying how the fluid phase and the solid matrix thermal gradient affect the thermal transport, flow properties, and overall heat performance. Numerical techniques are employed to explore the enhanced thermal behavior of nanofluids and their interaction with porous media under LTNE conditions. The flow velocity variations are more significant with the thermophoretic and Brownian motion parameters, the internal heat source, and the inverse Darcy number than with the local thermal non-equilibrium parameters, such as the interphase heat-transfer coefficient and the thermal diffusivity ratio. The temperature profiles of the fluid and solid phases vary remarkably over an intermediate finite range of LTNE parameters, where LTNE is prominent. For large values of LTNE parameters (<span>(Hrightarrow infty ,gamma rightarrow infty )</span>), the LTNE effect ceases, and the temperature profiles of the individual phases become independent of these parameters and converge asymptotically towards local thermal equilibrium results. Remarkably, the influence of LTNE diminishes for large values of the interfacial heat transfer coefficient and the ratio of thermal diffusivities, as observed in convective instability problems.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic stability of swelling porous elastic systems with nonstandard nonlinear kelvin–voigt damping","authors":"Adel M. Al-Mahdi, Mohammad M. Al-Gharabli","doi":"10.1007/s11565-026-00674-9","DOIUrl":"10.1007/s11565-026-00674-9","url":null,"abstract":"<div><p>In this paper, we investigate the long-time behavior of a swelling porous elasticity system incorporating a single nonstandard nonlinear Kelvin–Voigt damping mechanism. This type of damping, which acts through a nonlinear viscoelastic law, significantly influences the dissipative structure of the system. By carefully analyzing the behavior of the damping term near the origin, we derive an explicit and general decay rate formula for the energy functional. Our results reveal that the nonlinear damping is sufficiently strong to stabilize the system asymptotically, even in the absence of additional damping sources. To the best of our knowledge, this is the first work that considers this specific form of damping in the context of swelling porous media. The findings of this study constitute a novel contribution to the field and improve upon several existing results in the literature.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Towards a function theory of complexified octonions","authors":"Rolf Sören Kraußhar, Heikki Orelma","doi":"10.1007/s11565-026-00712-6","DOIUrl":"10.1007/s11565-026-00712-6","url":null,"abstract":"<div><p>In this article we study function theory in the 16-dimensional space of complexified octonions <span>(mathbb {O}_{mathbb {C}}=mathbb {C}otimes mathbb {O})</span>. We define the complexified octonionic Cauchy–Riemann operator </p><div><div><span>$$ D=sum _{j=0}^7 e_jpartial _{z_j} $$</span></div></div><p>where <span>(partial _{z_j}{:=}partial _{x_j}+ipartial _{y_j})</span> for <span>(j=0,1,...,7)</span>. This operator together with its octonionic conjugate factorize the ultrahyperbolic operator </p><div><div><span>$$ mathcal {L}=Doverline{D}=overline{D}D=sum _{j=0}^7 partial _{z_j}^2. $$</span></div></div><p>In real coordinates we obtain a Lichnerowicz-Weitzenböck type formula of the form </p><div><div><span>$$ mathcal {L} = Delta _x - Delta _y + 2i langle partial _x, partial _y rangle $$</span></div></div><p>One main goal of this paper consists in investigating the fundamental solution and polynomial solutions of the operator <span>(mathcal {L})</span>. The set of polynomial solutions is completely described by proposing explicit basis constructions and dimension formulae. Another main goal that is to carefully figure out in detail how complexified octonion analysis precisely differs from classical real octonion analysis in 8 dimensions. We explain some really substantial differences. In particular, the component functions are not Euclidean harmonic but ultrahyperbolic harmonic exhibiting a very different regularity behavior. Furthermore, the classical Fischer-decomposition is not anymore true in this context.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00712-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bounds for the zeros of a quaternionic polynomial","authors":"Ishfaq Ahmad Wani, Abdul Liman, Tanweer Jalal","doi":"10.1007/s11565-026-00710-8","DOIUrl":"10.1007/s11565-026-00710-8","url":null,"abstract":"<div><p>In this paper, we obtain new bounds for the zeros of a quaternionic polynomial by implementing the maximum modulus theorem within the system of regular quaternionic setting. Using structural properties of zero sets adapted to the non-commutative setting, we derive explicit areas that contain all zeros of the polynomial. The obtained results extend and refine several known localization theorems for quaternionic polynomials. In particular, we generalize existing results concerning the location and distribution of zeros for quaternionic polynomials with real coefficients to a broader class.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}