<abstract> <p>This paper introduces a novel numerical scheme, the conformable finite difference method (CFDM), for solving time-fractional gas dynamics equations. The was developed by integrating with derivatives, offering unique approach to tackle challenges posed models. study explores significance of such equations in capturing physical phenomena like explosions, detonation, condensation moving flow, and combustion. stability proposed scheme is rigorously investigated,...

In this study, we present a numerical method named the logarithmic non-polynomial spline method. This combines conformable derivative, finite difference, and techniques to solve nonlinear inhomogeneous time-fractional Burgers–Huxley equation. The developed scheme is characterized by sixth-order convergence conditional stability. accuracy of demonstrated with 3D mesh plots, while effects time fractional order are shown in 2D plots. Comparative evaluations cubic B-spline collocation provided....

In this study, the sequential operator of mixed order is analysed on domain (μ2,μ1)∈(0,1)×(0,1) with 1<μ2+μ1<2. Then, positivity nabla obtained analytically a finite time scale under some conditions. As consequence, our analytical results are introduced set, named Em,ζ, which monotonicity analysis obtained. Due to complicatedness set Em,ζ several numerical simulations so applied estimate structure and they provided by means heat maps.

A B-spline is defined by the degree and quantity of knots, it observed to provide a higher level flexibility in curve surface layout. The extended cubic (ExCBS) functions with new approximation for second derivative finite difference technique are incorporated this study solve time-fractional Allen–Cahn equation (TFACE). Initially, Caputo’s formula used discretize derivative, while ExCBS spatial derivative’s discretization. Convergence analysis carried out stability proposed method also...

Asymmetry plays a significant role in the transmission dynamics novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none developed models that incorporate different symmetry developmental stages. This paper introduces Taylor monomial falling function presents some properties of this delta model with Green’s kernel. In deterministic case, will be non-negative, shows has an upper bound for its maximum point. More precisely, paper, based on...

There is a strong correlation between the concept of convexity and symmetry. One these class interval-valued cr-log-h-convex functions, which closely related to theory In this paper, we obtain Hermite–Hadamard its weighted version inequalities that are some known results recaptured. To support our main results, offer three examples two applications modified Bessel functions special means as well.

The time-fractional coupled Korteweg–De Vries equations (TFCKdVEs) serve as a vital framework for modeling diverse real-world phenomena, encompassing wave propagation and the dynamics of shallow water waves on viscous fluid. This paper introduces precise resilient numerical approach, termed Conformable Hyperbolic Non-Polynomial Spline Method (CHNPSM), solving TFCKdVEs. method leverages inherent symmetry in structure TFCKdVEs, exploiting conformable derivatives hyperbolic non-polynomial...

&lt;abstract&gt; &lt;p&gt;In this paper, we suggest the Rishi transform, which may be used to find analytic (exact) solution multi-high-order linear fractional differential equations, where Riemann-Liouville and Caputo derivatives are used. We first developed transform of foundational mathematical functions for purpose then described important characteristics applied solve ordinary equations equations. Following that, found an exact a particular example looked at four numerical problems...

Abstract Making use of the Hankel determinant and Ruscheweyh derivative, in this work, we consider a general subclass m -fold symmetric normalized biunivalent functions defined open unit disk. Moreover, investigate bounds for second class some consequences results are presented. In addition, to demonstrate accuracy on conditions, most programs written Python V.3.8.8 (2021).

Abstract The Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class $\Sigma_{m}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> m -fold symmetric bi-univalent analytic functions. Estimates initial Taylor-Maclaurin coefficients $\vert a_{m+1} \vert $ <mml:mo>|</mml:mo> <mml:mi>a</mml:mi> <mml:mrow> <mml:mo>+</mml:mo>...

We consider the Stokes problem in a square or cube provided with nonstandard boundary conditions which involve normal component of velocity and tangential components vorticity. write variational formulation this three independent unknowns: vorticity, velocity, pressure. Next, we propose discretization by spectral methods relies on and, since it leads to an inf-sup condition pressure natural way, prove optimal error estimates for unknowns. present numerical experiments are perfect coherence analysis.

This paper presents a new general subfamily NΣmu,v(η,μ,γ,ℓ) of the family Σm that contains holomorphic normalized m-fold symmetric bi-univalent functions in open unit disk D associated with Ruscheweyh derivative operator. For belonging to introduced here, we find estimates Taylor–Maclaurin coefficients am+1 and a2m+1, consequences results are discussed. The current findings both extend enhance certain recent studies this field, specific scenarios, they also establish several connections...

This study investigates the stability behavior of nonlinear Fredholm and Volterra integral equations, as well integro-differential equations with terms, through lens symmetry principles in mathematical analysis. By leveraging fixed-point methods within b-metric spaces, which generalize classical metric spaces while preserving structural symmetry, we establish sufficient conditions for Hyers–Ulam–Rassias Hyers–Ulam stability. The symmetric framework offers a unified approach to analyzing...

This study introduces novel concepts of convergence and summability for numerical sequences, grounded in the newly formulated deferred Nörlund density, explores their intrinsic connections to symmetry mathematical structures. By leveraging principles inherent sequence behavior employing two distinct modulus functions under varying conditions, profound links between are established. The further incorporates lacunary refinements, enhancing understanding statistical its symmetric properties....

This study investigates the stability of a three-dimensional cubic functional equation within several mathematical frameworks, including $(n, \beta)$-normed spaces, non-Archimedean and random normed spaces. The theoretical results are validated through experimental approaches, offering practical insight into behavior these equations. A comparative analysis is provided, highlighting differences in dynamics across various Notably, introduction spaces their counterparts presents novel framework...

The discretization of initial and boundary value problems their existence behaviors are great significance in various fields. This paper explores the a class self-adjoint delta fractional difference equations. study begins by demonstrating uniqueness an problem Riemann–Liouville operator type. Based on this result, equation will be examined determined. Next, we define Cauchy function based differences. Accordingly, solution investigated according to function. Furthermore, research...

Abstract In this paper, we deal with topology optimization attributed to the non stationary Navier-Stokes equations. We propose an approach where analyze sensitivity of a shape function relating perturbation flow domain. A numerical algorithm based on topological gradient method is built and applied 2D Tesla micro valve reconstruction. Some results confirm efficiency proposed approach.

The structural changes along the c axis, of Ba-exchanged montmorillonite (Swy-2-Ba), under variable relative humidity (% RH), is investigated. In this regard, arrangement, amount and position both exchangeable cation water molecules in interlamellar space (IS), are evaluated. This aim achieved using X-ray diffraction (XRD) profile modeling approach that consists comparing experimental theoretical patterns calculated from models. contributions hydration states interlayer amounts, as a...

The analytical soliton solutions place a lot of value on birefringent fibres. major goal this study is to generate novel forms for the Radhakrishnan-Kundu-Lakshmanan equation, which depicts unstable optical solitons that arise from propagations using (presumably new) extended direct algebraic (EDA) technique used here extract large number RKLE. It gives up thirty-seven, essentially correspond all families. This method's ability determine many sorts through single process one its key...

&lt;abstract&gt;&lt;p&gt;In this paper, we proposed some new integral inequalities for subadditive functions and the product of functions. Additionally, a novel identity was established number Hermite-Hadamard type pertinent to tempered fractional integrals were proved. Finally, support major results, provided several examples corresponding graphs newly inequalities.&lt;/p&gt;&lt;/abstract&gt;

Abstract In this work, we handle a time-dependent Navier-Stokes problem in dimension three with mixed boundary conditions. The variational formulation is written considering independent unknowns: vorticity, velocity, and pressure. We use the backward Euler scheme for time discretization spectral method space discretization. present complete numerical analysis linked to formulation, which leads us priori error estimate.

Singular singularly-perturbed problems (SSPPs) are a powerful mathematical tool for modelling variety of real phenomena, such as nuclear reactions, heat explosions, mechanics, and hydrodynamics. In this paper, the numerical solutions to fourth-order singular boundary initial value presented using novel quintic B-spline (QBS) approximation approach. This method uses quasi-linearization approach solve SSPNL initial/boundary problems. And non-linear transformed into sequence linear by applying...