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Showing 1 to 15 of 15 for “"fractional differential equations"”.
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Wavelets operational methods for fractional differential equations and systems of fractional differential equations
… 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 matrix of fractional order derivative and integration based on this polynomial was also developed and used …
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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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A Study on the Feasibility of Using Fractional Differential Equations for Roll Damping Models
An optimization algorithm has been developed to study the effectiveness of substituting time tested ODEs with FDEs as applied to ship motions, specifically with an eye toward modeling different forms of roll damping. Relations between the order of differentiation a and damping coefficient b in the …
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ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES
… we present a generalization to two existing fractional integrals and derivatives, namely, the Riemann-Liouville and Hadamard fractional operators. The existence and uniqueness results for single term fractional differential equations (FDE) have also been established. We also obtain the Mellin …
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Development of Fractional Trigonometry and an Application of Fractional Calculus to Pharmacokinetic Model
… 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. <br />The main …
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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 …
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On Differential Equations With Indefinite Principal Parts
… with problems arising from a study of various differential equations with indefinite principal parts whether they be classified as ordinary, abstract, or fractional. In the first paper (Chapter 2) we show that Sturm’s separation theorem always fails for a classical real two term second order …
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Sir epidemic and predator - prey models of fractional-order
… mathematical models such as ordinary differential equations have been extended to fractional models, which are transformed using fractional differential equations. It was believed that these fractional models are more realistic to represent the daily life phenomena. The main focus of …
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Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels
… solids. In Part I of this thesis, we utilize fractional differential equations, formulated into fractional constitutive models, to describe the strain and rate-dependence of the stress response in complex fluids. This formulation is capable of quantitatively modeling the linear viscoelastic …
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Rheological Methods and Their Application To Biological Systems
… adequate for the two material types studied, a fractional viscoelastic model is found to be far superior for pectin in vitro. Fractional viscoelasticity is the use of fractional differential equations for the modelling of viscoelastic phenomena. In addition to its aforementioned use for pectin, …
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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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A Multigrid Acceleration for an ADI Finite Difference Method for Two-Dimensional Space Fractional Diffusion Equations
<p>Fractional diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. Because of the nonlocal property of fractional differential operators, the numerical methods for fractional …
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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 …