<abstract><p>We present new Mercer variants of Hermite-Hadamard (HH) type inequalities via Atangana-Baleanu (AB) fractional integral operators pertaining non-local and non-singular kernels. We establish trapezoidal identities for operator involving kernel give Jensen-Mercer (JM) differentiable mapping $ \Upsilon possessing convex absolute derivatives. connections our results with several renowned in the literature also applications to special functions.</p></abstract>

In this scholarly exploration, we employ new mapping method to unveil soliton solutions the nonlinear fractional Kudryashov's equation, using β-derivative and M-Truncated derivatives. Soliton phenomena, invaluable for enhancing computational capabilities in computer systems, find particular utility tasks like data analysis, image processing, simulations across various science domains. Our research reveals diverse solution forms, encompassing dark, periodic, kink, singular, dark-bright,...

In this paper, we establish a new auxiliary identity of the Bullen type for twice-differentiable functions in terms fractional integral operators. Based on identity, some generalized Bullen-type inequalities are obtained by employing convexity properties. Concrete examples given to illustrate results, and correctness is confirmed graphical analysis. An analysis provided estimations bounds. According calculations, improved Hölder power mean give better upper-bound results than classical...

Abstract A key paradigm in contemporary research is the use of graphs to represent physical systems, molecular structures, or particularly metal frameworks. Graphs are increasingly widely used a variety fields, including study quantum and macromolecules their interactions, socioeconomic ecological technical infra‐structural systems. Understanding how these systems function, robust, stable begins with structural characterization. The entropies entropy‐like measurements graphs/structures...

Abstract Topological indices are the fixed numbers associated with graphs. In recent years, mathematicians used to check pharmacology characteristics and molecular behavior of medicines. this article first Zagreb connection number index is computed for nanotubes VC 5 C 7 [ p , q ] HC Boron triangular Nanotubes. Also, same Quadrilateral section $P_{m}^{n}$ $P_{m+\frac{1}{2}}^{n}$ cuts from regular hexagonal lattices.

The (2 + 1)-dimensional Konopelchenko-Dubrovsky system contributes to the field of atmospheric science by investigating behaviour nonlinear waves, revealing subtle scattering effects and extended-range interactions within tropical mid-latitude troposphere. This equation provides insights into interplay between equatorial Rossby capturing their complex dynamics. Nonlinear waves are significant in processes understanding dynamics is important for comprehending weather patterns. study centres...

Many researchers have been attracted to the study of convex analysis theory due both facts, theoretical significance, and applications in optimization, economics, other fields, which has led numerous improvements extensions subject over years. An essential part mathematical inequalities is function its extensions. In recent past, Jensen–Mercer inequality Hermite–Hadamard–Mercer type remained a topic interest inequalities. this paper, we several for GA-h-convex functions subclasses, including...

<p>Superquadratic function is a generalization of convex functions. Results based on superquadratic functions are more refined than the results obtained using notion convexity. This work aims to provide new class called fuzzy-interval-valued (superquadrtic $ F_{I.V.F} $) and demonstrate its properties fuzzy order relations. In space intervals, this relation also termed as Kulisch-Miranker defined such level-wise. By leveraging definition features superquadrtic $, we come up with...

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with and helpful in featuring properties. Among these descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical In this article, eccentric connectivity, total augmented first Zagreb eccentricity, modified second edge version indices, graph PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, explicit...

Several graph invariants have been defined and studied, which present applications in nanochemistry, computer networks, other areas of science. One vastly studied class the is topological indices, helps studies chemical, biological, physical properties a chemical structure. recently introduced invariant face index, can assist predicting energy boiling points certain structures. In this paper, we drive analytical closed formulas index silicon carbides <mml:math...

Abstract It is interesting to study the molecular topology that provides a base for relationship of physicochemical property definite molecule. The molecule and irregularity structure plays vital character in shaping properties like enthalpy entropy. In this article, we are interested calculate some irregular topological indices two classes metal organic frameworks (MOFs) namely BHT (Butylated hydroxytoluene) based (M = Co, Fe, Mn, Cr) (MBHT) M1TPyP-M2 (TPyP 5, 10, 15, 20-tetrakis...

Irregularity indices are usually used for quantitative characterization of the topological structures non-regular graphs. In numerous problems and applications, especially in fields chemistry material engineering, it is useful to be aware irregularity a molecular structure. Furthermore, evaluation graphs valuable not only structure-property relationship (QSPR) structure-activity (QSAR) studies but also various physical chemical properties, including entropy, enthalpy vaporization, melting...

Topological indices (TIs) transform a molecular graph into number. The TIs are vital tool for quantitative structure activity relationship (QSAR) and quantity property (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical network <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mtext>HCB</mtext> <mfenced open="(" close=")" separators="|"> <mrow> <mi>r</mi> </mrow> </mfenced> </math> vertical obtained by identification vertices first rows with...

The use of information–theoretical methodologies to assess graph-based systems has received a significant amount attention. Evaluating graph’s structural information content is classic issue in fields such as cybernetics, pattern recognition, mathematical chemistry, and computational physics. Therefore, conventional methods for determining rely heavily on specific partitioning the vertex set obtain probability distribution. A network’s entropy based distribution obtained from partitioning....

Fractional calculus is extremely important and should not be undervalued due to its critical role in the theory of inequalities. In this article, different generalized Hermite-Hadamard type inequalities for functions whose modulus first derivatives are (α,s)-convex presented, via Caputo-Fabrizio integrals. Graphical justifications main results presented. Graphs enable us support our conclusions show reliability findings. Additionally, some applications probability numerical integration also...

In this article, we study the zero-divisor graphs Γ(Zn) of rings integers modulo n as information systems I(Γ(Zn)) using equivalence classes and rough sets. Equivalence are referred granules partitions indiscernible partitions. We define an indiscernibility relation on vertex set identify different sets attributes that induce same partition. A reduct is a minimal subset which yields partition original attribute set. compute all reducts defined system classify them in to two types including:...

In this manuscript, we demonstrate a graphical comparison analysis of the classical, quantum, and symmetric quantum derivatives for any continuous function, evaluated at $\mathfrak{z}=1$ $\mathtt{q}=0.5$ . We introduce new notions Hahn calculus give basic interpretations derivative integration function in calculus. This enable us to derive general Hölder's inequality as an application, extract corresponding Minkowski's settings. Later, construct exciting Lemma which power rule An example is...

For a (molecular) graph <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>G</mml:mi></mml:math>, the first and second entire Zagreb indices are defined by formulas id="M2"><mml:mrow><mml:msubsup><mml:mi>M</mml:mi><mml:mn>1</mml:mn><mml:mi>ε</mml:mi></mml:msubsup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:msub><mml:mrow><mml:mo...

In quantitative structure-property relationship (QSPR) and structure-activity (QSAR) studies, computation of topological indices is a vital tool to predict biochemical physio-chemical properties chemical structures. Numerous have been inaugurated describe different features. The ev ve-degree are recently introduced novelties, having stronger prediction ability. this article, we derive formulae the ev-degree based for structure <i>Si</i>₂<i>C</i>₃ − <i>I</i>[<i>a</i>,<i>b</i>].

This paper focuses on the comparative study of natural convection flow fractional Maxwell fluid having uniform heat flux and radiation. The well‐known equation with an integer‐order derivative has been extended to a non‐integer‐order derivative, i.e., derivative. explicit expression for temperature velocity is acquired by utilizing Laplace transform (LT) technique. two concepts are used (Caputo Caputo–Fabrizio derivatives) in formulation problem. Utilizing Mathcad programming, effect certain...

One of the most recent advancements in graph theory is use a multidisciplinary approach to investigation specific structural dependent features, such as physico-chemical properties, biological activity and entropy measure representing objects like network or chemical compound. The ability measures determine both certainty uncertainty about makes them one investigated topics science along with its nature. As result, many formulae, based on vertices, edges symmetry, for determining graphs have...

Abstract In recent years, several structure-based properties of the molecular graphs are understood through chemical graph theory. The <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>G</m:mi></m:math> G a molecule consists vertices and edges, where represent atoms in edges bonds between these atoms. A numerical quantity that gives information related to topology is called topological index. Several indices, contributing theory, have been defined vastly studied. Recent inclusions...