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369 articles for “fractionizing”
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Lyapunov-Stable Adaptive Fractional-Order Interval Type-2 Fuzzy Control for Robust Anti-Lock Braking Under Uncertain Road Adhesion Conditions
Abstract: This paper proposes a Lyapunov-stable Adaptive Fractional-Order Interval Type-2 Fuzzy Logic Controller (FO-IT2FLC) for robust anti-lock braking system (ABS) control under nonlinear vehicle dynamics and uncertain road adhesion conditions. The proposed framework integrates fractional-order error dynamics to capture memory-dependent tire–road interaction, interval Type-2 fuzzy inference to model uncertainty via footprint-of-uncertainty representation, and a Lyapunov-based adaptive learning mechanism for real-time parameter tuning. A rigorous stability proof guarantees boundedness of all closed-loop …
Published in Journal of Control & Instrumentation · Vol. 17, Issue 2, 2026 · pp. 31–41 Read article
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The Rise of Fractional Calculus: Novel Applications in Engineering and Biological Systems
Abstract: Fractional calculus (FC) is an advanced mathematical framework that generalizes the classical concepts of differentiation and integration to non-integer, or fractional, orders. This extension of traditional calculus allows for the modeling of complex dynamic systems that exhibit behavior not easily captured by integer-order differential equations. Over the last few decades, fractional calculus has seen a rapid rise in popularity, particularly in applied mathematics, engineering, and biological sciences, due to its …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 7–11 Read article
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Review on Fractional Order Sliding Mode Control of Nonlinear System
Abstract: This paper presents review fractional order sliding mode control of nonlinear system.Sliding mode control (SMC) may be a variable structure control (VSC). It is a nonlinear manipulates approach that approaches in supplied,an impact action andrestricts plant to manage to feature in accordance to some pre-defined ordinary dynamic. This desired dynamic is mentioned as sliding surface. When plant follows sliding surface, it is in sliding mode.Fractional sliding mode control (FSMC) is …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 8, Issue 1, 2021 · pp. 8–16 Read article
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Theoretical Analysis of Volume/Weight Fraction of a Dual-Constituent Composite
Abstract: Conventional equations used in analysis of composite materials are modelled based on volume-averaging principle. The volume-averaging equations were re-evaluated to provide an alternative weight-averaging consideration as a result of the difficulty in practical determination of volume fraction of individual constituents of composite material, especially particulate composite. The equivalent weight-averaging equation analysis showed that density plays a significant determining factor in material selection of individual constituent; and composite density evaluated using …
Published in Journal of Polymer & Composites · Vol. 5, Issue 1, 2017 · pp. 32–39 Read article
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Advance Fixed Point Theorems and Its Application to Ordinary and Fractional Differential Equations
Abstract: In the present research, advanced results on the fixed point theorem are applied to typical boundary value problems. Finding a differential equation's solution under certain boundary conditions is the goal of typical boundary value topics. The article appears to extend new fixed point results to a new context, likely involving fractional operators with unique kernels, notably the Caputo-type fractional operator. This extension involves applying the fixed point theorem to a …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 1–15 Read article
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Development of Software Packages for Computer Aided Design and Performance Analysis of Industrial Fractional Distillation Equipment
Abstract: This paper deals with improved CAD software packages that have been developed with the objective of improvising the existing conservative design of fractional distillation equipment. Since fractional distillation is extensively employed in petroleum refineries, distilleries and in a large number of chemical process industries, accurate design and optimised performance of these equipments are detrimental to the overall economy of these industries. Further, the efficient performance of the fractionators are dependent …
Published in Emerging Trends in Chemical Engineering · Vol. 2, Issue 3, 2015 · pp. 15–41 Read article
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Control of BLDC Motor using Fractional-order PID Controller Optimized by ICA
Abstract: In this paper a new method for speed control of BLDC motors is proposed. In this method, fractional order PID (FOPID) is used for control of BLDC motor. In order to determine the parameters of FOPID controller imperialist competitive algorithm (ICA) is employed for its high speed and accurate for solve of optimization problems. In order to verify the performance of proposed controller, some simulations have been carried out with …
Published in Journal of Power Electronics and Power Systems · Vol. 3, Issue 3, 2013 · pp. 27–38 Read article
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Fractional Calculus-Based Analysis of Magneto-Thermal Nanofluid Flow Over Stretching and Shrinking Surfaces
Abstract: This study presents a comprehensive investigation of magneto-thermal hybrid nanofluid flow over stretching and shrinking surfaces using a fractional calculus framework to capture the memory and hereditary characteristics of complex fluid transport phenomena. The proposed model incorporates the effects of magnetic field intensity, thermal radiation, viscous dissipation, Brownian motion, and thermophoretic diffusion on the velocity and temperature distributions within the boundary layer region. A fractional-order derivative formulation is employed to …
Published in Recent Trends in Fluid Mechanics · Vol. 13, Issue 2, 2026 · pp. 1–10 Read article
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Tensile and Flexural Strength Quantification of Basalt-Reinforced Epoxy Composites Fabricated via Vacuum-Assisted Resin Transfer Molding at Varied Fiber Volume Fractions Description
Abstract: Fiber-reinforced polymer composites have been identified to possess excellent properties that render them very suitable in the aerospace, automotive, marine and renewable energy sectors. However, for the industrially scalable vacuum-assisted resin transfer molding (VARTM) process, optimization of mechanical properties of basalt epoxy composites must be achieved systematically, which means that the effect of the fiber volume fraction (VF) on the mechanical properties of the composite needs to be quantified for …
Published in Journal of Polymer & Composites · Vol. 14, Issue 4, 2026 · pp. 43–57 Read article
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Comparative of Encryption-Decryption Performance of (Binary, Gray- Scale, Color) Images Using Discrete Fractional Fourier Transform (DFRFT)
Abstract: The Discrete Fractional Fourier transform (DFRFT) provides an effective model of image encryption by further developing the classic Fourier transform by adding fractional orders, which increase the degrees of freedom. Owing to the omnipresence of digital media in many industries like education, healthcare, and entertainment, the mobility of visual data has become a significant issue to keep confidential. Images form one of the main ways of exchanging information and, therefore, …
Published in Research & Reviews : Journal of Physics · Vol. 15, Issue 1, 2026 · pp. 54–65 Read article
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Computable Extension of New Advanced Fractional Kinetic Equation
Abstract: AbstractFirst, we obtain computable extensions of advanced fractional kinetic equation. The aim of this survey is to explore the behavior of physical and biological systems from the point of view of fractional calculus. Fractional calculus, integration and differentiation of an arbitrary or fractional order, provide new tools that expand the descriptive power of calculus beyond the familiar integer-order concepts of rates of change and area under a curve. Fractional calculus …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 26–32 Read article
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Fractional q-Derivative and N2 Function
Abstract: AbstractThe study of fractional q-calculus in this paper serves as a bridge between the fractional q-calculus in the literature and the fractional q-calculus of Special Functions. This paper is devoted to fractional q-derivative of special functions. Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, physics, or other applications in engineering .To begin with the theorem on …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 41–43 Read article
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Induction of Specific Cytotoxic Lymphocytes in Goats Vaccinated with Fractionated Antigens of Brucella melitensis 16M
Abstract: The present study investigated the ability of different fractionated antigens of Brucella melitensis 16M to induce cytotoxic T-lymphocytes. For this study, soluble Lipopolysaccharide and outer membrane protein antigens were fractionated by using gel filtration chromatography and found 6, 5 and 5 fractions respectively of each antigen. All the regions of antigens were analyzed for their ability to induce cytotoxic T-lymphocytes. This study investigated that SAG5, LPG1 and OMPG4 induce maximum …
Published in Research and Reviews : A Journal of Biotechnology · Vol. 3, Issue 2, 2013 · pp. 12–18 Read article
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Fractional Riemannian Fuzzy C-Means with Time-Series Regularization for Economic Manifold Forecasting
Abstract: A fractional Riemannian fuzzy c-means framework is proposed for uncertain economic forecasting on non-Euclidean data domains. Observations are represented on a Riemannian manifold, cluster centres are intrinsic prototypes, and a latent fuzzy regime signal is regularised by both autoregressive and fractional-memory penalties. The resulting objective couples geometric clustering with time-series consistency, thereby discouraging partitions that are locally plausible but temporally incoherent. Closed-form membership updates, exponential-map centre updates, normal equations for …
Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 49–55 Read article
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Advanced Computable Extension of New Fractional Kinetic Equation
Abstract: AbstractThe aim of this work is to find advanced computable extension of kinetic equation with fractional calculus approach. Fractional calculus originated in 1695, shortly after the inversion of classical calculus. The pioneer researchers who studied it were Liouville, Riemann, Leibniz, etc. For a long time, fractional calculus has been regarded as a pure mathematical area without applications. But, in recent decades, such type of synergism has been changed. It has …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 3, 2017 · pp. 74–80 Read article
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FRACTIONAL q-DERIVATIVE AND GENERALIZED K-FUNCTION
Abstract: AbstractThis investigation is basically intended to fractional q-derivative of special functions. In this article we drive the results on term by term q-fractional differentiation of a generalized k-Series. As particular case we will obtain the fractional q-differentiation of the power series and exponential series. To start with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 6–9 Read article
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Effect of Aluminium Mole Fraction on the AlGaN/GaN HEMTs with 10 nm AlGaN Nano-Layer
Abstract: We report the effect of aluminium mole fraction on drain current in AlGaN/GaN high electron mobility transistors (HEMTs). The drain current increases with the drain voltage. Also, the effect of gate voltage on drain current as well as the effect of drain voltage on source current is studied. The drain current is invariant and nearly 0 mA corresponding to the aluminium mole fractions of 0.10, 0.15, 0.20, and 0.25 related …
Published in Journal of Microelectronics and Solid State Devices · Vol. 3, Issue 3, 2016 · pp. 15–21 Read article
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On the Fractional Calculus Operators and DefiniteResults Including N2-Function
Abstract: In this present paper, fractional Riemann-Liouville calculus operators of a new special function called N2-function is introduced given by author has been obtained. This function is a modified form of Mittag-Leffler function [1]. The author drives the results between N2-function and fractional operators. Cite this Article:Mohd. Farman Ali, Manoj Sharma, Renu Jain. On the Fractional Calculus Operators and Definite Results Including N2-Function. Research & Reviews: Discrete Mathematical Structures. 2015; 2(2): …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 2, Issue 2, 2015 · pp. 5–9 Read article
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Dirichlet Average of New Generalized M-series and Fractional Calculus
Abstract: AbstractWe know that every analytic function can be measured as a Dirichlet average and connected with fractional calculus. In this note, we set up a relation between Dirichlet average of new generalized M-series, and fractional derivative. Fractional derivative is a derivative of arbitrary order i.e. may be real, complex, integer or fractional order.Keywords: Dirichlet average new generalized M-series, fractional derivative, fractional calculus operatorsCite this ArticleManoj Sharma. Dirichlet Average of New …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 3, Issue 3, 2016 · pp. 13–16 Read article
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Modified Riemann−Liouville Fractional Derivative and Differential Equation for a Class of New Levy-type Probabilities
Abstract: The aim of the present paper to obtained the solution of differential equations involving Modified Riemann-Liouville fractional derivative in addition to it Levy-type one sided probability density function. Some scientist studied a small number of interesting problems regarding diffusing processes in media with fractal geometry, and formulated fractional diffusion.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 3, 2014 · pp. 42–44 Read article