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46 articles for “fractional derivative”
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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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An Application of Fractional Calculus in L-R and C-R Circuit
Abstract: In this paper, we proposed a Fractional differential equation for the electrical L-R and C-R Circuit and obtained the solution in the form of Mittag-Leffler function.Keywords: Circuit analysis, L-R and C-R circuit, Fractional differential equation, Riemann-Liouville Fractional derivative, Laplace transform, Inverse Laplace transform.Mathematical Subject Classification: -26A33, 33E12, 44A10Cite this Article: Laxmi Morya, Manoj Sharma, Rajshree Mishra. An Application of Fractional Calculus in L-R andC-R Circuit. Research & Reviews: Discrete Mathematical …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 7, Issue 2, 2020 · pp. 14–17 Read article
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FD and DDA of N2 Function
Abstract: The object of the present paper is to establish the results of Double Dirichlet average (DDA) of N2 Function, using Riemann-Liouville Fractional derivative (FD). This function is a modified form of Mittag-Leffler function [15]. The author drives the results between N2-function and fractional operators. The N2 Function can be measured as a Dirichlet average and connected with fractional calculus. In this paper the solution comes in compact form of double …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 5, Issue 2, 2018 · pp. 34–39 Read article
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INTEGRAL REPRESENTATION OF K-FUNCTION
Abstract: Abstract: In this article, an attempt to be made to introduce the four-different integral representation of Extended K-function and special cases have also been discussed [1, 2]. The Extended K Function which is introduced by the authors first time in this work is extended version of earlier K-Function of Sharma [3]. We will use Riemann-Liouville fractional calculus operator in finding the integral representation of this extended K- Function. Fractional Calculus …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 3, 2017 · pp. 81–88 Read article
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Modified Milk Fat and Its Applications in Food Products
Abstract: Natural fats have complex composition as they are composed of several fatty acids present primarily as triacylglycerols, which give fat highly diverse functional and nutritional properties. This complexity of fat provides opportunities for modifying themselves for different applications. The negative nutritional and physical image of the fat, especially certain saturated long chain fatty acids, trans-fats, cholesterol as well as poor spreadability and oxidative susceptibility has driven the development of technologies …
Published in Research and Reviews : Journal of Dairy Science and Technology · Vol. 2, Issue 3, 2013 · pp. 16–24 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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On the Time Fractional Natural Convection Flow of Incompressible Viscous Fluid Past Vertical Plate
Abstract: Time fractional partial differential equations governing the free convective flow of an incompressible viscous fluid over vertical plate with Newtonian heating and mass diffusion in the presence of first order chemical reaction are derived by using fractional complex transforms. The dimensionless temperature, concentration and velocity field and the rate of heat and mass transfer from the plate to the field are determined using Laplace transform. The similarly solution for ordinary …
Published in Research & Reviews : Journal of Physics · Vol. 8, Issue 2, 2019 · pp. 69–74 Read article
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Mannan-Rich Fractions in Poultry Nutrition: A Sustainable and Defensive Strategy against Antimicrobial Resistance
Abstract: Antimicrobial resistance (AMR) has evolved to be a significant global threat, menacing worldwide health and food security. Its proliferation in poultry farming has spurred the search for sustainable, non-antibiotic alternatives. One promising alternative is Mannan-Rich Fractions (MRFs), which is derived from Saccharomyces cerevisiae. These bioactive compounds not only support poultry health but also aid in suppressing pathogenic bacteria without contributing to resistance. This review brings together current studies highlighting how …
Published in Recent Trends in Infectious Diseases · Vol. 3, Issue 2, 2026 · pp. 1–16 Read article
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Neural Network Based Fractional Order PID Controller for Harmonic Mitigation of Induction Motor Drive System
Abstract: Torque produced in IM (induction Motor) is collected fundamental torque, however, due to core saturation, air gap irregularity, and winding distribution; stator and rotor slotting harmonics torque are produced. This reduces the quality of the power system, life span, and performance of the motor and the controller device. In this paper, a neural network, based fractional order proportional integral derivative (NNFOPID) controller is designed to compensate the harmonics of the …
Published in International Journal of Electrical Power and Machine Systems · Vol. 1, Issue 1, 2023 · pp. 23–41 Read article
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Removal of Thiophene from Model Fuel Using Titanium Catalyst
Abstract: Organosulfur compounds like thiophene (Th) and its alkyl derivatives are the major unwanted species present in crude oil fractions as they lead to the formation of sulfur oxides after combustion of the fuel and these oxides of sulfur cause severe environmental damage. Oxidative desulfurization (ODS) process is considered as one of the best alternative deep desulfurization technologies compared to hydrodesulfurization. In the ODS process, the sulfur compounds are oxidized to …
Published in Journal of Modern Chemistry & Chemical Technology · Vol. 7, Issue 1, 2016 · pp. 31–36 Read article
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Evaluation of Coefficient of Performance of Water– Carrol Vapor Absorption Refrigeration System Using Artificial Neural Network approach
Abstract: Normal 0 false false false EN-US X-NONE X-NONE The aim of this work is to apply expert system methods, like artificial neural network (ANN), for evaluating the coefficient of performance (COP) of water-carrol (lithium bromide-ethylene glycol)-based vapor absorption refrigeration system. Theoretical performance analysis of vapor absorption refrigeration system is too complex since very tedious second-order mathematical differential equations are used. In order to simplify this complex process, artificial neural networks …
Published in Trends in Mechanical Engineering & Technology · Vol. 2, Issue 3, 2012 · pp. 29–37 Read article
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Influence of Aspect Ratio on the Mechanical and Tribological Properties of Vertical Centrifugal Cast Aluminium Silicon Alloy
Abstract: To get a sound cast of precise shape and size in the vertical centrifugal casting process, the flow behavior of the melt and process parameters such as aspect ratio of the mould, rotating speed, volume fraction, etc. must be optimized. The optimal parameters of the vertical centrifugal casting process derived from past cold modelling studies in casting of Al-12%Si alloy are investigated in this paper. Casts were obtained using 7 …
Published in Journal of Polymer & Composites · Vol. 11, Issue 13, 2023 · pp. 104–111 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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Novel Characteristics of GaN based Nanoelectronic Double-Heterojunction HEMTs to Establish a Solid-State-Electronics Laboratory
Abstract: The drain characteristics are investigated with respect to electrical variables (drain voltage, gate voltage) and structural parameters of high electron mobility transistors (HEMTs). Total 10526 individual simulation-outputs are reported in this work. The maximum drain current of 553 mA is achieved by the simulated structures of double-heterojunction HEMTs using the SILVACO-ATLAS software tool. The drain current is higher at shorter gate length. The drain current is higher at larger aluminium …
Published in Journal of Semiconductor Devices and Circuits · Vol. 4, Issue 3, 2017 · pp. 11–20 Read article
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Physics-Informed Machine Learning and Multiscale Modeling for Structure–Property Quantification of Polymer Composites
Abstract: The growing need for light-weight, high strength, and sustainable polymer composites has led to the development of smart methods that enable accurate structural-property quantification and material design. However, conventional methods have been predominantly data-based, thus ignoring physical constraints as well as multi-scale interactions involving fiber, matrix, interface, and process parameters, leading to lower accuracy and poor robustness and interpretability of the models. In this study, a Cat Swarm Optimization-Tuned Physics-Informed …
Published in Journal of Polymer & Composites · Vol. 14, Issue 4, 2026 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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Stress Analysis of Two-Dimensional Functionally Graded Thick Rotating Disks by Element Based Material Grading
Abstract: The present study reports the stress and deformation analysis of thick rotating disks made of two-dimensional functionally graded materials (FGMs). The analysis is carried out using element based gradation of material properties in radial and axial direction over the discretized domain. Material properties are distributed according to power law distribution and the governing equations are derived using principle of stationary total potential (PSTP). The resulting deformation and stresses are evaluated …
Published in Journal of Experimental & Applied Mechanics · Vol. 8, Issue 1, 2017 · pp. 28–36 Read article
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Gallium Nitride based HEMTs in Nano-Scale Regime
Abstract: AbstractIn this work, a maximum drain current of 557 mA is achieved by the simulated structures of double-heterojunction HEMTs using the SILVACO-ATLAS software tool. The drain current is found to be higher at shorter gate length. The drain current is observed as higher at larger aluminium mole fraction. The drain current is also higher at larger thickness of AlGaN barrier layer. Again, the drain current is higher at larger doping …
Published in Journal of Microelectronics and Solid State Devices · Vol. 5, Issue 3, 2018 · pp. 11–21 Read article
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An Investigation of Stress and Deformation States of Rotating Functionally Graded Spherical Pressure Vessels
Abstract: The present study deals with the analysis of rotating spherical pressure vessels made of functionally graded materials (FGMs). Material properties are graded along the radial direction, which is achieved by varying volume fractions of the constituting materials according to Mori-Tanaka scheme. Shells are subjected to hydrostatic internal pressure and have free boundary condition at the outer surface. Governing equations are derived using principle of stationary total potential. The effects of …
Published in Journal of Experimental & Applied Mechanics · Vol. 8, Issue 3, 2017 · pp. 19–27 Read article
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Thermoacoustic Properties of 1-Propanol-n-Hexane and 1-Propanol-Cyclohexane Binary Mixtures: A Comparative Study at 298.15 K
Abstract: This study reports the measurement of ultrasonic velocity (U), viscosity (η), and density (ρ) for the binary liquid mixtures 1-propanol–n-hexane and 1-propanol–cyclohexane at 298.15 K over the full composition range (mole fraction 0.1–0.9). From the experimentally measured data, several important thermodynamic and acoustic parameters, including isentropic compressibility (βₐ), acoustic impedance, intermolecular free length, free volume (Vf), and internal pressure (πᵢ), were systematically derived to assess the magnitude and nature of …
Published in Journal of Modern Chemistry & Chemical Technology · Vol. 17, Issue 1, 2026 · pp. 19–31 Read article