Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 26 for “"fractional derivative"”.
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Fractional derivative models and their use in the characterization of hydropolymer and in-vivo breast tissue viscoelasticity
… few as three parameters using the Kelvin-Voigt Fractional Derivative (KVFD) modeling approach. We propose to image these parameters for simulated and experimental imaging phantoms and to estimate them for normal and cancerous in-vivo breast tissues. After a detailed presentation of the …
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Simulation of the fractional derivative operator [square root of] s and the fractional integral operator 1 [divided by the square root of] s
Digitized by Kansas State University Libraries
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Fractional calculus operator and its applications to certain classes of analytic functions. A study on fractional derivative operator in analytic and multivalent functions.
… thesis is to obtain numerous applications of fractional derivative operator concerning analytic and -valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a …
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Numerical methods for fractional differential equations by new caputo and hadamard types operators
Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-Fabrizio operator, Caputo-Hadamard fractional …
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Unsteady newtonian and non-newtonian fluid flows in the circular tube in the presence of magnetic field using caputo-fabrizio derivative
… were solved using the Caputo-Fabrizio time fractional order model without singular kernel. The analytical solutions were obtained using Laplace transform, finite Hankel transforms and Robotnov and Hartley’s functions. The velocity profiles obtained from various physiological parameters were …
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Nonlinear vibration analysis of viscoelastic plates with fractional damping
Fractional calculus has the history as long as the classical calculus, but up to recent years, less attention has been paid to this method due to its complexity and difficulties in dealing with fractional derivatives and fractional integrals. In the present study, the nonlinear vibration analysis …
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Seismic Response of Structures with Added Viscoelastic Dampers
… the frequency dependence of the damper. The fractional derivative model and the general linear model are capable of capturing the frequency dependence of viscoelastic materials accurately. In our research, therefore, we have focused on the development of systematic procedures for calculating …
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Existence of Positive Solutions to a Family of Fractional Two-Point Boundary Value Problems
<p>In this paper we will consider an nth order fractional boundary value problem with boundary conditions that include a fractional derivative at 1. We will develop properties of the Green's Function for this boundary value problem and use these properties along with the Contraction Mapping …
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Efficient schemes on solving fractional integro-differential equations
Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after. …
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Wavelets operational methods for fractional differential equations and systems of fractional differential equations
… an effective and simple operational matrix of derivative was first derived and applied together with collocation method to solve some singular second order differential equations of Emden-Fowler type, a class of generalized Pantograph equations and Delay differential systems. A new operational …
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Non-Poissonian statistics, aging and "blinking'" quantum dots.
… It is shown that this aging property in the fractional derivative formalism forces to introduce a fractional index depending on time. It is shown also that, when a stationary condition exists, the Onsager regression principle is fulfilled only if the system is aged and consequently if an …
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Mechanical Modelling of single and collective cells behavior
… which combines classical and spring-pot based (fractional derivative) models is presented. Than the modelling has been enriched considering the non-linear effect of the prestress, induced in protein filaments during cell adhesion and in the cell membrane (with a simple multiscale scheme that …
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Estimates for solutions to the Dysthe equation and numerical simulations of walking droplets in harmonic potentials
… uniformly in space the L² norm in time of a fractional derivative of the linear solution by the L² norm in space of the initial data. This section of the thesis lays the groundwork for further developments in proving well-posedness via a contraction argument.
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Development of Fractional Trigonometry and an Application of Fractional Calculus to Pharmacokinetic Model
… may ask what would be the 1/2-th or square root derivative of x. Fractional calculus generalize the operation of differentiation and integration to non-integer orders. Although it seems not to have significant applications, research on this subject could be valuable in understanding the nature. …
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Effects of fractional time derivatives in predator-prey models
This thesis is concerned with the effects of fractional derivatives in predator-prey like systems, including models of plant water interaction. In Chapter 3, a fractional order predator-prey model is introduced, and we show how fractional derivative order can change the system from monostable to …
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Quantifying non-Fickian transport in porous and fractured media using fractional-calculus based stochastic models
… requires parsimonious models such as the fractional engine based physical models. In this dissertation, I first compared three types of time non-local transport models, which include the multi-rate mass transfer (MRMT) model, the continuous time random walk (CTRW) framework, and the …
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Time-Domain Simulation of Sound Propagation in Frequency-Dependent Materials
… may contain either convolution operation or fractional derivative operation. Both operations have been studied in this dissertation. Recursive algorithm methods, piece-wise constant recursive methods (PCRC) and piece-wise linear recursive methods (PLRC) are used to numerically solve for …
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Analysis in Fractional Calculus and Asymptotics Related to Zeta Functions
… -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders. Dating back to Leibniz, this idea was considered by many great mathematical figures, and in recent decades it has been used to model many real-world systems …
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Soft tissue viscoelastic properties: measurements, models and interpretation
… using a concise feature set. The Kelvin-Voigt fractional derivative (KVFD) model introduced in this study represents the measurement data of a broad range in both time and frequency domain with a small number of parameters, and it yields stable estimates for many types of phantoms and tissues. …
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The Dynamic Foundation of Fractal Operators.
The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most …
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