Search results for: Girsanov Theorem
159 The Proof of Analogous Results for Martingales and Partial Differential Equations Options Price Valuation Formulas Using Stochastic Differential Equation Models in Finance
Authors: H. D. Ibrahim, H. C. Chinwenyi, A. H. Usman
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Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.
Keywords: Option price valuation, Martingales, Partial Differential Equations, PDEs, Equivalent Martingale Measure, Girsanov Theorem, Feyman-Kac Theorem, European Put Option.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 378158 On the Maximum Theorem: A Constructive Analysis
Authors: Yasuhito Tanaka
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We examine the maximum theorem by Berge from the point of view of Bishop style constructive mathematics. We will show an approximate version of the maximum theorem and the maximum theorem for functions with sequentially locally at most one maximum.Keywords: Maximum theorem, Constructive mathematics, Sequentially locally at most one maximum.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1968157 Fermat’s Last Theorem a Simple Demonstration
Authors: Jose William Porras Ferreira
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This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power and power and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between and power through the Pascal’s triangle or Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:
zn=xn+yn for n>2 and (x, y, z) E Z+ - {0}
Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2993156 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem
Authors: Adil AL-Rammahi
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In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.
Keywords: Fredholm integral equation, power series, Banach fixed point theorem, Linear Systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2486155 Positive Solutions for Semipositone Discrete Eigenvalue Problems via Three Critical Points Theorem
Authors: Benshi Zhu
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In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional.Keywords: Discrete eigenvalue problems, positive solutions, semipositone, three critical points theorem
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1251154 Constructive Proof of Tychonoff’s Fixed Point Theorem for Sequentially Locally Non-Constant Functions
Authors: Yasuhito Tanaka
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We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.
Keywords: sequentially locally non-constant functions, Tychonoff’s fixed point theorem, constructive mathematics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1502153 The Martingale Options Price Valuation for European Puts Using Stochastic Differential Equation Models
Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed
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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.
Keywords: Equivalent Martingale Measure, European Put Option, Girsanov Theorem, Martingales, Monte Carlo method, option price valuation, option price valuation formula.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 729152 Weyl Type Theorem and the Fuglede Property
Authors: M. H. M. Rashid
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Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge Transformation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 551151 Extremal Properties of Generalized Class of Close-to-convex Functions
Authors: Norlyda Mohamed, Daud Mohamad, Shaharuddin Cik Soh
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Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .Keywords: Argument of f ′(z) , Carathéodory Function, Closeto- convex Function, Distortion Theorem, Extremal Properties
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1352150 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets
Authors: Menglong Su, Shaoyun Shi, Qing Xu
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In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.
Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1440149 A Sandwich-type Theorem with Applications to Univalent Functions
Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal
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In the present paper, we obtain a sandwich-type theorem. As applications of our main result, we discuss the univalence and starlikeness of analytic functions in terms of certain differential subordinations and differential inequalities.Keywords: Univalent function, Starlike function, Differential subordination, Differential superordination.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1318148 On the Central Limit Theorems for Forward and Backward Martingales
Authors: Yilun Shang
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Let {Xi}i≥1 be a martingale difference sequence with Xi = Si - Si-1. Under some regularity conditions, we show that (X2 1+· · ·+X2N n)-1/2SNn is asymptotically normal, where {Ni}i≥1 is a sequence of positive integer-valued random variables tending to infinity. In a similar manner, a backward (or reverse) martingale central limit theorem with random indices is provided.Keywords: central limit theorem, martingale difference sequence, backward martingale.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2777147 Cryptographic Attack on Lucas Based Cryptosystems Using Chinese Remainder Theorem
Authors: Tze Jin Wong, Lee Feng Koo, Pang Hung Yiu
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Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC3 cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC4,6 cryptosystem than LUC3 and LUC cryptosystems. Current study concludes that LUC4,6 cryptosystem is more secure than LUC and LUC3 cryptosystems in sustaining against Lenstra’s attack.Keywords: Lucas sequence, Dickson Polynomial, faulty signature, corresponding signature, congruence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 728146 Reduction of Search Space by Applying Controlled Genetic Operators for Weight Constrained Shortest Path Problem
Authors: A.K.M. Khaled Ahsan Talukder, Taibun Nessa, Kaushik Roy
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The weight constrained shortest path problem (WCSPP) is one of most several known basic problems in combinatorial optimization. Because of its importance in many areas of applications such as computer science, engineering and operations research, many researchers have extensively studied the WCSPP. This paper mainly concentrates on the reduction of total search space for finding WCSP using some existing Genetic Algorithm (GA). For this purpose, some controlled schemes of genetic operators are adopted on list chromosome representation. This approach gives a near optimum solution with smaller elapsed generation than classical GA technique. From further analysis on the matter, a new generalized schema theorem is also developed from the philosophy of Holland-s theorem.Keywords: Genetic Algorithm, Evolutionary Optimization, Multi Objective Optimization, Non-linear Schema Theorem, WCSPP.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1409145 Recursive Wiener-Khintchine Theorem
Authors: Khalid M. Aamir, Mohammad A. Maud
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Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).
Keywords: Power Spectral Density (PSD), Wiener-KhintchineTheorem, Periodogram, Short Time Fourier Transform (STFT), TheSliding DFT.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2481144 Some Applications of Gröbner bases
Authors: Hassan Noori, Abdolali Basiri, Sajjad Rahmany
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In this paper we will introduce a brief introduction to theory of Gr¨obner bases and some applications of Gr¨obner bases to graph coloring problem, automatic geometric theorem proving and cryptography.Keywords: Gr¨obner bases, Application of Gr¨obner bases, Automatic Geometric Theorem Proving, Graph Coloring, Cryptography.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4912143 Quadrilateral Decomposition by Two-Ear Property Resulting in CAD Segmentation
Authors: Maharavo Randrianarivony
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The objective is to split a simply connected polygon into a set of convex quadrilaterals without inserting new boundary nodes. The presented approach consists in repeatedly removing quadrilaterals from the polygon. Theoretical results pertaining to quadrangulation of simply connected polygons are derived from the usual 2-ear theorem. It produces a quadrangulation technique with O(n) number of quadrilaterals. The theoretical methodology is supplemented by practical results and CAD surface segmentation.Keywords: Quadrangulation, simply connected, two-ear theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1252142 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem
Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit
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We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.
Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1726141 Periodic Solutions for a Third-order p-Laplacian Functional Differential Equation
Authors: Yanling Zhu, Kai Wang
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By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g t, 0 −τ x(t + s) dα(s) + e(t), some criteria to guarantee the existence of periodic solutions are obtained.
Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1285140 Lagrange-s Inversion Theorem and Infiltration
Authors: Pushpa N. Rathie, Prabhata K. Swamee, André L. B. Cavalcante, Luan Carlos de S. M. Ozelim
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Implicit equations play a crucial role in Engineering. Based on this importance, several techniques have been applied to solve this particular class of equations. When it comes to practical applications, in general, iterative procedures are taken into account. On the other hand, with the improvement of computers, other numerical methods have been developed to provide a more straightforward methodology of solution. Analytical exact approaches seem to have been continuously neglected due to the difficulty inherent in their application; notwithstanding, they are indispensable to validate numerical routines. Lagrange-s Inversion Theorem is a simple mathematical tool which has proved to be widely applicable to engineering problems. In short, it provides the solution to implicit equations by means of an infinite series. To show the validity of this method, the tree-parameter infiltration equation is, for the first time, analytically and exactly solved. After manipulating these series, closed-form solutions are presented as H-functions.Keywords: Green-Ampt Equation, Lagrange's Inversion Theorem, Talsma-Parlange Equation, Three-Parameter Infiltration Equation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1885139 Multiple Positive Periodic Solutions to a Predator-prey system with Harvesting Terms and Holling II Type Functional Response
Authors: Pan Wang, Yongkun Li
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In this paper, a periodic predator-prey system with harvesting terms and Holling II type functional response is considered. Sufficient criteria for the existence of at least sixteen periodic solutions are established by using the well known continuation theorem due to Mawhin. An example is given to illustrate the main result.
Keywords: Periodic solution, predator-prey system, harvesting terms, continuation theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1282138 A new Configurable Decimation Filter using Pascal-s Triangle Theorem
Authors: A. Chahardah Cherik, E. Farshidi
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This paper presents a new configurable decimation filter for sigma-delta modulators. The filter employs the Pascal-s triangle-s theorem for building the coefficients of non-recursive decimation filters. The filter can be connected to the back-end of various modulators with different output accuracy. In this work two methods are shown and then compared from area occupation viewpoint. First method uses the memory and the second one employs Pascal-s triangle-s method, aiming to reduce required gates. XILINX ISE v10 is used for implementation and confirmation the filter.Keywords: Decimation filter, sigma delta, Pascal's triangle'stheorem, memory
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1678137 PI Control for Second Order Delay System with Tuning Parameter Optimization
Authors: R. Farkh, K. Laabidi, M. Ksouri
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In this paper, we consider the control of time delay system by Proportional-Integral (PI) controller. By Using the Hermite- Biehler theorem, which is applicable to quasi-polynomials, we seek a stability region of the controller for first order delay systems. The essence of this work resides in the extension of this approach to second order delay system, in the determination of its stability region and the computation of the PI optimum parameters. We have used the genetic algorithms to lead the complexity of the optimization problem.Keywords: Genetic algorithm, Hermit-Biehler theorem, optimization, PI controller, second order delay system, stability region.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1772136 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator
Authors: Lv Yuhua
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In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1427135 Simplified Equations for Rigidity and Lateral Deflection for Reinforced Concrete Cantilever Shear Walls
Authors: Anas M. Fares
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Reinforced concrete shear walls are the most frequently used forms of lateral resisting structural elements. These walls may take many forms due to their functions and locations in the building. In Palestine, the most lateral resisting forces construction forms is the cantilever shear walls system. It is thus of prime importance to study the rigidity of these walls. The virtual work theorem is used to derive the total lateral deflection of cantilever shear walls due to flexural and shear deformation. The case of neglecting the shear deformation in the walls is also studied, and it is found that the wall height to length aspect ratio (H/B) plays a major role in calculating the lateral deflection and the rigidity of such walls. When the H/B is more than or equal to 3.7, the shear deformation may be neglected from the calculation of the lateral deflection. Moreover, the walls with the same material properties, same lateral load value, and same aspect ratio, shall have the same of both the lateral deflection and the rigidity. Finally, an equation to calculate the total rigidity and total deflection of such walls is derived by using the virtual work theorem for a cantilever beam.Keywords: Cantilever shear walls, flexural deformation, lateral deflection, lateral loads, reinforced concrete shear walls, rigidity, shear deformation, virtual work theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5019134 The Boundary Theory between Laminar and Turbulent Flows
Authors: Tomasz M. Jankowski
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The basis of this paper is the assumption, that graviton is a measurable entity of molecular gravitational acceleration and this is not a hypothetical entity. The adoption of this assumption as an axiom is tantamount to fully opening the previously locked door to the boundary theory between laminar and turbulent flows. It leads to the theorem, that the division of flows of Newtonian (viscous) fluids into laminar and turbulent is true only, if the fluid is influenced by a powerful, external force field. The mathematical interpretation of this theorem, presented in this paper shows, that the boundary between laminar and turbulent flow can be determined theoretically. This is a novelty, because thus far the said boundary was determined empirically only and the reasons for its existence were unknown.Keywords: Freed gravitons, free gravitons.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1460133 Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory
Authors: Ping Liu, Yongkun Li
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This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.
Keywords: Enterprise cluster, permanence, extinction, impulsive, comparison theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1453132 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation
Authors: Fengxia Zheng, Chuanyun Gu
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By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1481131 Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition
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This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.
Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1652130 Positive Periodic Solutions for a Predator-prey Model with Modified Leslie-Gower Holling-type II Schemes and a Deviating Argument
Authors: Yanling Zhu, Kai Wang
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In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.
Keywords: Predator-prey model, Holling II type functional response, positive periodic solution, coincidence degree theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1460