In this research, we aim to explore generalizations of Hardy-type inequalities using nabla Hölder’s inequality, nabla Jensen’s inequality, chain rule on nabla calculus and leveraging the properties of convex and submultiplicative fun...
In this paper, we prove some new generalized inequalities of Hilbert-type on time scales nabla calculus by applying Hölder’s inequality, Young’s inequality, and Jensen’s inequality. Symmetrical properties play an essential role...
In this study, we apply Hölder’s inequality, Jensen’s inequality, chain rule and the properties of convex functions and submultiplicative functions to develop an innovative category of dynamic Hardy-type inequalities on time scales d...
This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson’s type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Hölder’...
In this article, we establish several new generalized Hardy-type inequalities involving several functions on time-scale nabla calculus. Furthermore, we derive some new multidimensional Hardy-type inequalities on time scales nabla calculus. The main r...
In this paper, Hardy–Leindler, Hardy–Yang and Hwang type inequalities are extended on time scales calculus. These extensions are depending upon use of symmetric multiple delta integrals. The target is achieved by utilizing some inequaliti...
This work presents new results concerning weighted Hardy-type inequalities within the framework of delta conformable fractional integrals on arbitrary time scales. The proposed approach unifies the treatment of inequalities across continuous and disc...
Through the paper, we present several inequalities involving C-monotonic functions with C≥1, on nabla calculus via time scales. It is known that dynamic inequalities generate many different inequalities in different calculus. The main results will...
In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann–Liouville sense. We also introduce the nabla fractional derivative in Grünwald–Letnikov sense. Some of the basic proper...
Geodesics have a fundamental role in the geometry of curved surfaces, as well as in discrete geometry. We present the time scale analogy of the dynamic data sets parameterized by a tensor product of two times scales. The goal of our study is the find...
In this article, using a (γ,a)-nabla conformable integral on time scales, we study several novel Hilbert-type dynamic inequalities via nabla time scales calculus. Our results generalize various inequalities on time scales, unifying and extendin...
This paper introduces novel generalizations of dynamic inequalities of Copson type within the framework of time scales delta calculus. The proposed generalizations leverage mathematical tools such as Hölder’s inequality, Minkowski’s...
In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals of time scale calculus. These extensions are used to generalize Hardy-type inequalities with general kernels via diamond...
In this article, we prove several new fractional nabla Bennett–Leindler dynamic inequalities with the help of a simple consequence of Keller’s chain rule, integration by parts, mean inequalities and Hölder’s inequality for the...
In this article, we developed the idea of q-time scale calculus in quantum geometry. It includes the q-time scale integral operators and ∆q-differentials. It analyzes the fundamental principles which follow the calculus of q-time scales co...
The question raised in the title of the article is not philosophical. We do not expect general answers of the form “to describe the reality surrounding us”. The question should actually be formulated as a mathematical problem of applied m...
In this paper, we present a generalization of Radon’s inequality on dynamic time scale calculus, which is widely studied by many authors and an intrinsic inequality. Further, we present the classical Bergström’s inequality and refine...
In this article, we establish some new generalized inequalities of the Hilbert-type on time scales’ delta calculus, which can be considered similar to formulas for inequalities of Hilbert type. The major innovation point is to establish some dy...
This work presents refined and generalized forms of weighted Opial-type inequalities within the framework of time scale calculus. The proofs rely on several algebraic techniques, together with Hölder’s inequality and Keller’s chain r...
This paper is concerned with some new Hermite-Hadamard inequalities on two types of time scales, Z and Nc,h. Based on the substitution rules, we first prove the discrete Hermite-Hadamard inequalities on Z relating to the midpoint a+b2 and extend them...
We prove new Hardy–Copson-type (γ,a)-nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller’s chain rule, the integration by parts formula, and the dynamic Hölder inequality on time scales....
We introduce the Levinson functional on time scales using integral inequality of Levinson’s type in the terms of Δ-integral for convex (concave) functions on time scale sets and investigate its properties such as superadditivity and monot...
In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales T. We achieve this by utilizing Hölder’s inequality, the chain rule, and the mean inequality. As specific instances of our finding...
We investigated several novel conformable fractional gamma-nabla dynamic Hardy–Hilbert inequalities on time scales in this study. Several continuous inequalities and their corresponding discrete analogues in the literature are combined and expa...
This paper examines fractional multi-time scale stochastic functional differential equations that, in addition, are driven by fractional noises. Based on a specially crafted fixed-point principle for the so-called “local operators”, we pr...
This research investigates innovative extensions of Hardy-type inequalities through the use of nabla Hölder’s and nabla Jensen’s inequalities, combined with the nabla chain rule and the characteristics of convex and submultiplicative...
Building on the work of Josip Pečarić in 2013 and 1982 and on the work of Srivastava in 2017. We prove some new α-conformable dynamic inequalities of Steffensen-type on time scales. In the case when α=1, we obtain some well-known time scale inequalit...
In this article, we will prove some new diamond alpha Hilbert-type dynamic inequalities on time scales which are defined as a linear combination of the nabla and delta integrals. These inequalities extend some known dynamic inequalities on time scale...
In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and thei...
In this work, Noether symmetries and conserved quantities of a non-standard Birkhoffian system based on the Caputo Δ Pfaff–Birkhoff principle on time scales are studied. Firstly, equations of motion for Caputo Δ non-standard Birkhof...
In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive σ-finite measures in time s...
In this paper, we introduce a comprehensive and expanded framework for generalized calculus and generalized polynomials in discrete calculus. Our focus is on (q;h)-time scales. Our proposed approach encompasses both difference and quantum problems, m...
Our work in this paper is based on the reverse Hölder-type dynamic inequalities illustrated by El-Deeb in 2018 and the reverse Hilbert-type dynamic inequalities illustrated by Rezk in 2021 and 2022. With the help of Specht’s ratio, the con...
The calculus in the absence of limits is known as quantum calculus. With a difference operator, it substitutes the classical derivative, which permits dealing with sets of functions that are non-differentiations. The theory of integral inequality in...
In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When α = 1 we obtain some we...
In this paper, we propose two fractional-order calculus-based data augmentation methods for audio signals. The first approach is based on fractional differentiation of the Mel scale. By using a randomly selected fractional derivation order, we are wa...
Financial time series have a fractal nature that poses challenges for their dynamical characterization. The Dow Jones Industrial Average (DJIA) is one of the most influential financial indices, and due to its importance, it is adopted as a test bed f...
In this article, we discuss several novel generalized Ostrowski-type inequalities for functions whose derivative module is relatively convex in time scales calculus. Our core findings are proved by using the integration by parts technique, Hölde...
This paper mainly deals with introducing and studying the properties of generalized nabla differentiability for fuzzy functions on time scales via Hukuhara difference. Further, we obtain embedding results on E n for generalized nabla differen...
In this article, we survey the sensor network calculus (SensorNC), a framework continuously developed since 2005 to support the predictable design, control and management of large-scale wireless sensor networks with timing constraints. It is rooted i...
Several inverse integral inequalities were proved in 2004 by Yong. It is our aim in this paper to extend these inequalities to time scales. Furthermore, we also apply our inequalities to discrete and continuous calculus to obtain some new inequalitie...
In this survey paper, we present both some basic properties of the four-parameters Wright function and its applications in Fractional Calculus. For applications in Fractional Calculus, the four-parameters Wright function of the second kind is especia...
The scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. An apparent corollary of this law is the scaling of physiologic time with body size, implying that physiologic time is separate a...
Fractional calculus-based differential equations were found by previous studies to be promising tools in simulating local-scale anomalous diffusion for pollutants transport in natural geological media (geomedia), but efficient models are still needed...
Our work is based on the multiple inequalities illustrated in 2020 by Hamiaz and Abuelela. With the help of a Fenchel-Legendre transform, which is used in various problems involving symmetry, we generalize a number of those inequalities to a general...
As an effective tool to unify discrete and continuous analysis, time scale calculus have been widely applied to study dynamic systems in both theoretical and practical aspects. In addition to such a classical role of unification, the dynamic equation...
The application of fractional calculus in the field of kinetic theory begins with questions raised by Bernoulli, Clausius, and Maxwell about the motion of molecules in gases and liquids. Causality, locality, and determinism underly the early work, wh...
In this paper, we present some Ostrowski–Grüss-type inequalities on time scales for functions whose derivatives are bounded by functions for k points via a parameter. The 2D versions of these inequalities are also presented. Our results ge...
We established some new α-conformable dynamic inequalities of Hardy–Knopp type. Some new generalizations of dynamic inequalities of α-conformable Hardy type in two variables on time scales are established. Furthermore, we investigat...
In order to merge continuous and discrete analyses, a number of dynamic derivative equations have been put out in the process of developing a time-scale calculus. The investigations that incorporated combined dynamic derivatives have led to the propo...
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