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.
Results
Showing 1 to 20 of 29 for “"fractional calculus"”.
-
Green's Functions of Discrete Fractional Calculus Boundary Value Problems and an Application of Discrete Fractional Calculus to a Pharmacokinetic Model
<p>Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete …
-
Discrete Fractional Calculus and Its Applications to Tumor Growth
… order up to the <i>n</i>-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make <i>n</i>- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate …
-
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 …
-
NABLA Fractional Calculus and Its Application in Analyzing Tumor Growth of Cancer
… we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to …
-
Development of Fractional Trigonometry and an Application of Fractional Calculus to Pharmacokinetic Model
… problems to mathematical expressions relies on calculus, which in turn relies on the differentiation and integration operations. We differentiate or integrate a function once, twice, or any whole number of times. But one may ask what would be the 1/2-th or square root derivative of x. Fractional …
-
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 …
-
Development of Nabla Fractional Calculus and a New Approach to Data Fitting in Time Dependent Cancer Therapeutic Study
<p>The aim of this thesis is to develop discrete fractional models of tumor growth for a given data and to estimate parameters of these models in order to have better data tting. We use discrete nabla fractional calculus because we believe the discrete counterpart of this mathematical theory will …
-
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 …
-
Analysis of Discrete Fractional Operators and Discrete Fractional Rheological Models
… two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about …
-
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 …
-
Modeling event-based coupled hydrologic and mass transport in small urban watersheds
… on model simulation. The application of fractional calculus to the advection-dispersion equation was also investigated for the distributed system model. A novel mass transport model based on a unit pollutograph (UP) concept analogous to the unit hydrograph (UH) theory was proposed and …
-
Scale-dependent homogenization of elastic-viscoelastic random composites
… shift of dominance of one phase over the other. Fractional calculus models are known to be robust descriptors of the behavior of real viscoelastic polymers. By allowing the derivative in viscoelastic constitutive relations to be of the fractional type, the response of a viscoelastic material can …
-
Fractional Order State Feedback Control for Improved Lateral Stability of Semi-Autonomous Commercial Heavy Vehicles
… investigates a new control scheme based on fractional calculus as a technique that ensures lateral stability of articulated large heavy vehicles during evasive highway maneuvering scenarios. The control method is first implemented to a passenger vehicle model with 2-axles based on the …
-
Study of the aging hereditariness of concrete through a novel viscoelastic formulation
… creep constitutive law based on variable-order fractional calculus, resulting in an excellent feature with respect to classical creep models. Indeed, the creep deformations obtained through the proposed model are very close to the deformations evaluated by means of Model B3. Moreover, the …
-
Fractional order models of the human respiratory system
The fractional calculus is a generalization of classical integer-order integration and derivation to fractional (non-integer) order operators. Fractional order (FO) models are those models which contain such fractional order operators. A common representation of these models is in frequency domain, …
-
Umbral Calculus A Different Mathematical Language
… differential equations, including those of fractional nature. It will provide an account of the theory and applications of Operational Methods allowing the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we are referring …
-
Towards Structural Health Monitoring of Gossamer Structures Using Conductive Polymer Nanocomposite Sensors
… Two mathematical models, based on the modified fractional calculus and the Preisach approaches, have been developed to model the variation of electrical resistance with strain in a conductive polymer. After that, a compensator based on a modified Preisach model has been developed. The …
-
A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction.
… transport in porous media can be modeled with fractional differential equations. This approach results in early arrival of contaminants and heavy-tail distributions observed in field experiments. The implicit finite difference scheme with the shifted Grunwald approximation discritizing the …
-
<strong>A Fractional Zener Constitutive Model to Describe the Degradation of Swine Cerebrum with Validation from Experimental Data and Predictions using Finite Element Analysis</strong>
… compressive rates was also considered.</p><p>The fractional Zener (FZ) constitutive model, which uses concepts from fractional calculus, was selected to predict the behavior of <em>postmortem</em> swine brain tissue. This model was defined in three-dimensional (3D) form to facilitate its use via …
Page 1 of 2