Fractional calculus

Part 1 of ebook "Stochastic processes and calculus: An elementary introduction with applications" provides readers with contents including: Chapter 1 - Introduction; Chapter 2 - Basic concepts from probability theory; Chapter 3 - Autoregressive moving average processes (ARMA); Chapter 4 - Spectra of stationary processes; Chapter 5 - Long memory and fractional integration; Chapter 6 - Processes with autoregressive conditional heteroskedasticity (ARCH);...

163p daonhiennhien 03-07-2024 1 1   Download

Ebook "Design of CMOS analog integrated fractional-order circuits: Applications in medicine and biology" describes the design and realization of analog fractional-order circuits, which are suitable for on-chip implementation, capable of low-voltage operation and electronic adjustment of their characteristics. The authors provide a brief introduction to fractional-order calculus, followed by design issues for fractional-order circuits of various orders and types.

118p lucchinguyen 28-12-2023 6 2   Download

The aim of this work is to study the tail distribution of the Cox–Ingersoll–Ross (CIR) model driven by fractional Brownian motion. We first prove the existence and uniqueness of the solution.

9p viberkshire 09-08-2023 9 5   Download

Ebook 3000 solved problems in calculus: Part 2 includes contents: Chapter 22 volume; chapter 23 the natural logarithm; chapter 24 exponential functions; chapter 25 L'Hopital's rule; chapter 26 exponential growth and decay; chapter 27 inverse trigonometric functions; chapter 28 integration by parts; chapter 29 trigonometric integrands and substitutions; chapter 30 integration of rational functions: the method of partial fractions; chapter 31 integrals for surface area, work, centroids; chapter 32 improper integrals;… Please refer to the documentation for more details.

286p haojiubujain01 06-06-2023 3 2   Download

Luận văn Thạc sĩ Toán học "Giải tích phân thứ và phương trình vi phân bậc phân số trong không gian sobolev bậc phân số" nhằm giúp người học hiểu và vận dụng được các kết quả chính trong tiền ấn phẩm của Giáo sư M. Yamamoto “Fractional calculus and time -fractional diferential equations: revisit and construction of a theory.

54p mitmit02 18-05-2023 14 5   Download

This paper considers a generalization of fractional Bessel type process. It is also a type of singular stochastic differential equations driven by fractional Brownian motion which has been studied by some authors.

7p viirenerosenfeld 02-06-2022 8 1   Download

The main goal of this paper is to study selected aspects of the space-Fractional Continuum Mechanical model (s-FCM) approximation. The considerations include the in-depth analysis of three generalized finite difference schemes, which are based on: (i) The rectangle rule, (ii) the trapezoidal rule, and (iii) Simpson’s (parabolas) rule, respectively. The analysis includes the dynamic (eigenvalues) response of the 1D s-FCM body.

7p guernsey 28-12-2021 4 0   Download

Lecture Calculus - Chapter 9: Computing derivatives. After studying this section will help you understand: we list and prove the rules first, they are rather easy to prove; let us state all five of them as one theorem, and prove it,...

14p diepchilang 22-08-2021 7 1   Download

This paper considersa generalization of fractional Bessel type process. It is also a type of singular stochastic differential equations driven by fractional Brownian motion which were studied by some authors. Undersome assumptions of coefficients, this equation has a unique positive solution.

7p nguaconbaynhay12 13-06-2021 18 1   Download

Một toán tử quạt (sectorial operator) A có phổ của nó chứa trong hình quạt Sω với số kλR (λ, A)k bị chặn đều bên ngoài hình quạt lớn hơn. Các toán tử này đóng vai trò nổi bật trong lý thuyết về phương trình vi phân và đạo hàm riêng elliptic và parabolic. Vào những năm 1960, các toán tử bậc phân số (fractional powers) Aα (với α ∈ C) của toán tử quạt A được định nghĩa. Mời các bạn cùng tìm hiểu.

75p capheviahe26 02-02-2021 21 2   Download

A study of non-commensurate fractional linear system is done in a parallel way to the commensurate case. A partial fraction decomposition is accomplished using a recursive procedure. Each partial fraction is inverted in two different ways. The decomposition integer/fractional is done also. Some examples are presented.

7p dayhoctainha 10-09-2020 14 0   Download

Motivated by the fact that the fractional Laplacean generates a wider choice of the interpolation curves than the Laplacean or bi-Laplacean, we propose a new non-local partial differential equation inspired by the Cahn-Hilliard model for recovering damaged parts of an image. We also note that our model is linear and that the computational costs are lower than those for the standard Cahn-Hilliard equation, while the inpainting results remain of high quality.

10p dayhoctainha 10-09-2020 17 0   Download

This paper combines the synergies of three mathematical and computational generalizations. The concepts of fractional calculus, memristor and information visualization extend the classical ideas of integro-differential calculus, electrical elements and data representation, respectively. The study embeds these notions in a common framework, with the objective of organizing and describing the "continuum" of fractional order elements (FOE).

11p dayhoctainha 10-09-2020 23 0   Download

This paper reveals and analyzes the frequency bifurcation phenomena in the fractional-order inductive power transfer (FOIPT) system with series-series compensation topology. Using fractional calculus theory and electric circuit theory, the circuit model of the series-series compensated FOIPT system is first proposed, then taking the case of a single variable fractional order as an example, three frequency analytical solutions of frequency bifurcation equation are solved by using Taylor expansion method.

8p dayhoctainha 10-09-2020 20 0   Download

This paper proposes two kinds of fractional-order autonomous circuits based on fractionalorder elements with order larger than one. The corresponding mathematical models are also established based on fractional calculus and their characteristics are analyzed based on circuit theory. Finally, circuit simulation are performed to verify the correctness of theoretical analysis.

9p dayhoctainha 10-09-2020 4 1   Download

The present study provides a generalization of event-based control to the field of fractional calculus, combining the benefits brought by the two approaches into an industrial-suitable control strategy. During recent years, control applications based on fractional order differintegral operators have gained more popularity due to their proven superior performance when compared to classical, integer order, control strategies.

13p dayhoctainha 10-09-2020 12 0   Download

Fractional calculus (FC) is widely used in many interdisciplinary branches of science due to its effectiveness in describing and investigating complicated phenomena. In this work, nonlinear dynamics for a new physical model using nonlocal fractional differential operator with singular kernel is introduced. New Routh-Hurwitz stability conditions are derived for the fractional case as the order lies in [0,2). The new and basic Routh-Hurwitz conditions are applied to the commensurate case. The local stability of the incommensurate orders is also discussed.

12p covid19 14-06-2020 28 2   Download

In this paper, we investigate the problem of finite-time guaranteed cost control of linear uncertain conformable fractional order systems. Firstly, a new cost function is defined. Then, by using some properties of conformable fractional calculus, some new sufficient conditions for the design of a state feedback controller that makes the closed-loop systems finite-time stable and guarantees an adequate cost level of performance is derived via linear matrix inequalities, therefore can be efficiently solved by using existing convex algorithms.

7p mangamanga 29-02-2020 25 0   Download

This paper discusses the continuous effect of the fractional order parameter of the Lu¨ system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time.

8p kethamoi1 17-11-2019 19 0   Download

The objective of this paper is to study the optimal control problem for the fractional tuberculosis (TB) infection model including the impact of diabetes and resistant strains. The governed model consists of 14 fractional-order (FO) equations. Four control variables are presented to minimize the cost of interventions. The fractional derivative is defined in the Atangana-Baleanu-Caputo (ABC) sense. New numerical schemes for simulating a FO optimal system with Mittag-Leffler kernels are presented.

13p caygaocaolon1 13-11-2019 12 1   Download