Bifurcation Problems for Generalized Beam Equations by Fosheng Wang

“…The proof of the main results relies heavily on calculus facts rather than such complicated arguments as Lyapunov-Schmidt reduction technique or Morse index theory from nonlinear functional analysis.…”
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Existence of Weak Solutions for Fractional Integrodifferential Equations with Multipoint Boundary Conditions by Haide Gou, Baolin Li

“…By combining the techniques of fractional calculus with measure of weak noncompactness and fixed point theorem, we establish the existence of weak solutions of multipoint boundary value problem for fractional integrodifferential equations.…”
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An improved meta-heuristic algorithm to optimize the fractional-order controller for an industrial manipulator with a parallelogram structure by Nazila Nikdel

“…Therefore, this article pursues two main objectives: 1) controlling the robotic system by presenting a method based on fractional-order calculus so that it can control the system despite its complexity and non-linearity, 2) presenting the meta-heuristic algorithm "Improved Grey Wolf" to optimize the system response.Methodology: First, the mathematical model of the robot is presented based on Lagrange rules, and then the fractional-order calculus is used to design the controller. …”
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A novel approach to Lyapunov stability of Caputo fractional dynamic equations on time scale using a new generalized derivative by Michael Precious Ineh, Edet Peter Akpan, Hossam A. Nabwey

“…The proposed framework extended beyond the limitations of traditional integer-order calculus, offering a more flexible and generalizable tool for researchers working with dynamic systems. …”
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Newman's Error Analysis (NEA) in Solving Computational Thinking Problems on Indefinite Integral Material by Lisa Lisa, Elmanani Simamora, Mulyono Mulyono, E. Elvis Napitupulu, Asmin Panjaitan

“… The initial abilities of students in the Integral Calculus course reveal that many have not yet grasped the fundamental concepts of integration. …”
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Reading and Calculation Neural Systems and Their Weighted Adaptive Use for Programming Skills by Joao Castelhano, Isabel C. Duarte, Joao Duraes, Henrique Madeira, Miguel Castelo-Branco

“…We hypothesize that calculus and reading brain networks provide joint underpinnings with distinctly weighted contributions which concern programming tasks, in particular concerning error identification. …”
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Fractional Coins and Fractional Derivatives by J. A. Tenreiro Machado

“…This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. …”
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On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics by M. De la Sen

“…The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.…”
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Gentzen and Temporal Sequents by Indrzejczak Andrzej

“…The second, called Multiple Sequent Calculus (MSC), was proposed in the beginning of the present century. …”
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Extensions of Ostrowski Type Inequalities via h-Integrals and s-Convexity by Khuram Ali Khan, Khalid Mahmood Awan, Allah Ditta, Ammara Nosheen, Rostin Mabela Matendo

“…In this paper, Hölder, Minkowski, and power mean inequalities are used to establish Ostrowski type inequalities for s-convex functions via h-calculus. The new inequalities are generalized versions of Ostrowski type inequalities available in literature.…”
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Chebyshev Wavelet Analysis by Emanuel Guariglia, Rodrigo Capobianco Guido

“…In particular, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry. Finally, we give two examples concerning the main properties proved.…”
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Bi-Univalent Function Classes Defined by Using a Second Einstein Function by Alaa H. El-Qadeem, Saleh A. Saleh, Mohamed A. Mamon

“…Motivated by q-calculus, subordination principle, and the second Einstein function, we define two families of bi-univalent analytic functions on the open unit disc of the complex plane. …”
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Certain invariant subspaces for operators with rich eigenvalues by Karim Seddighi

“…When n=1 and T ϵ B1(Ω) such that σ(T)=Ω¯ is a spectral set for T we use the functional calculus we have developed for such operators to give some infinite dimensional cyclic invariant subspaces for T.…”
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Necessary Condition for an Euler-Lagrange Equation on Time Scales by Monika Dryl, Delfim F. M. Torres

“…New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given.…”
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Comparative evaluation of oral hygiene status by using oral hygiene index, simplified oral hygiene index, and modified oral hygiene index: Revalidation of modified oral hygiene ind... by Subhash Garg, Sumbul Nasir

“…In 1960, Greene and Vermillion introduced the Oral Hygiene Index (OHI), which assessed debris and calculus on 12 tooth surfaces. In 1964, they proposed a Simplified Oral Hygiene Index (OHI-S), which evaluated only 6 surfaces of six index teeth. …”
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Decoding of periodontal screening and recording index by Dler Ali Kursheed, Faraedon Mohidden Zardawi, Hadi Mohammad Ismail, Aras Maruf Rauf, Sarhang Sarwat Gul

“…Methods: In this interventional clinical study, PSR criteria were obtained from 50 participants plus decoding of each PSR code such as percentage of bleeding (Bl), calculus (Cal) and pocket depth (PD) in each sextant. …”
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Qualitative financial modelling in fractal dimensions by Rami Ahmad El-Nabulsi, Waranont Anukool

“…The relationship between fractional calculus and fractals is well-known in the literature. …”
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Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations by Guanfeng Li, Yong Wang, Gejun Bao

“…We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous 𝒜-harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.…”
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Certain Sequence Spaces over the Non-Newtonian Complex Field by Sebiha Tekin, Feyzi Başar

“…It is known from functional analysis that in classical calculus, the sets , , , and of all bounded, convergent, null and -absolutely summable sequences are Banach spaces with their natural norms and they are complete according to the metric reduced from their norm, where . …”
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Generalized p,q-Gamma-type operators by Wen-Tao Cheng, Qing-Bo Cai

“…In the present paper, the generalized p,q-gamma-type operators based on p,q-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. …”
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