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Open Access Article
1 - Computational Method for Fractional-Order Stochastic Delay Differential Equations
Behrouz Parsa Moghaddam Zeynab Salamat Mostaghim Elham Alsaddat Hashemi ZadehDynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order s MoreDynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense. The computational method is based on bilinear spline interpolation and finite difference approximation. The convergence order of the proposed method investigated in the mean square norm and the accuracy of proposed scheme is analyzed in the perspective of the mean absolute error and experimental convergence order. The proposed method is considered in determining statistical indicators of Gompertzian and Nicholson models. The fractional stochastic delay Gompertzian equation is modeled for describing the growth process of a cancer and the fractional stochastic delay Nicholson equation is formulated for explaining a population dynamics of the well-known Nicholson blowflies in ecology. Manuscript profile -
Open Access Article
2 - Local Fractional Variational Yang-Laplace Method for solving local fractional partial differential Equations
homa afraz Jafar Saberi nadjafiIn the last decade, the theory of local fractional calculus has been successfully used to describe and solve fundamental science and engineering problems. In this article, the local fractional Yang-Laplace variational iteration method has been used for solving the local MoreIn the last decade, the theory of local fractional calculus has been successfully used to describe and solve fundamental science and engineering problems. In this article, the local fractional Yang-Laplace variational iteration method has been used for solving the local fractional partial differential equation on a cantor set. The non-differentiable exact and approximate solutions are obtained for kind of local fractional linear and nonlinear equations. It is shown that the used method is an efficient and easy method to implement for linear and nonlinear problems arising in science and engineering. In this article, we emphasize on the LFYLVM method which is a combination form of local fractional variational iteration method and Yang-Laplace transform. Most of the obtained solutions from this method are in series form that converge rapidly to exact or approximate solutions. Illustrative examples demonstrate that the method is able to reduce the volume of computation compared to the existing classical methods. Manuscript profile -
Open Access Article
3 - A numerical method based on Chelyshkov polynomials for solving fractional integro-differential equations
Reza DehghanIn this paper, Chelyshkov expansion approach is presented for solving Volterra fractional order integro-differential equations with Caputo derivative. By means of the properties of Chelyshkov polynomials and numerical integral formula , the solution of fractional integr MoreIn this paper, Chelyshkov expansion approach is presented for solving Volterra fractional order integro-differential equations with Caputo derivative. By means of the properties of Chelyshkov polynomials and numerical integral formula , the solution of fractional integro-differential equations reduced to the solution of algebraic equations. Then, by solving the system of algebraic equations, the solution of the differential-integral equation is presented as a function in the terms of Chelyshkov polynomials. Accuracy and error analysis have been investigated and since the accuracy of the obtained results for fractional integro-differential equations depends on the number of selected Chelyshkov polynomials therefore, with the increase in the number of Chelyshkov polynomials, we can achieve desirable accuracy step by step. All calculations are done by MATLAB software. Also, the numerical results of based on Chelyshkov polynomials method are compared with the results of some of the available methods for the validity, accuracy and efficiency of the technique. Manuscript profile -
Open Access Article
4 - A NUMERICAL SOLUTION FOR THE FRACTIONAL RAYLEIGH-STOKES PROBLEM BY SPACE-TIME RADIAL BASIS FUNCTIONS
Nafiseh Noghrei Asghar Kerayechian Alireza SoheiliIn this paper, we approximate the solution of two-dimensional Rayleigh-Stokes problem ‎for a heated generalized second grade fluid with fractional derivatives. This approximation is ‎based on the space-time radial basis functions (RBFs) and the Sinc quadrature r MoreIn this paper, we approximate the solution of two-dimensional Rayleigh-Stokes problem ‎for a heated generalized second grade fluid with fractional derivatives. This approximation is ‎based on the space-time radial basis functions (RBFs) and the Sinc quadrature rule. In this ‎method, we use Gaussian radial basis function and don't distinguish between time and place ‎variables and the collocation points have both the coordinates of time and space. We use the ‎Sinc quadrature rule with single exponential transformation to approximate the integral part of ‎fractional derivatives. The chosen fractional derivatives is Riemann – Liouville.‎This method is implemented on two examples with different values of the fractional ‎derivative order. Obtained results illustrate the effectiveness of our method and sh ow that ‎one can obtain accurate results with a small number of the collocation points for the radial ‎basis function. It should be noted that all calculations in this paper have been done using ‎Mathematica software.‎ Manuscript profile -
Open Access Article
5 - Introduction of fuzzy q-fractional derivative and its properties
Naser Mikael Vand Zahra NoeiaghdamThe quantum calculus or q-calculus begins with F. H. Jackson in the early twentieth century, but only recently it has aroused interest, due to high demand of mathematics that is modeling quantum computing and it has been an important subject for applied sciences . The q MoreThe quantum calculus or q-calculus begins with F. H. Jackson in the early twentieth century, but only recently it has aroused interest, due to high demand of mathematics that is modeling quantum computing and it has been an important subject for applied sciences . The quantum calculus is one of the applied and inter disciplinary sciences, which is more important than the classical calculus because in the standard calculus the definition of the derivative depends on the existence of limit but the quantum derivative in quantum calculus works without the definition of limit and for this reason the work with a quantum calculus is numerically faster and easier than the standard calculus. In this paper, fuzzy quantum derivative, fuzzy quantum fractional derivative in Caputo sense by using generalized Hukuhara difference and fuzzy quantum fractional integral of the Riemann-Liouville type are introduced, then the related theorems and properties are provided in details.These results occur in many applications as physics, quantum theory, number theory, statistical mechanics, etc. Manuscript profile -
Open Access Article
6 - The generalized variational iteration method to solve the fractal partial differential equations
Homa Afraz Alireza Khalili GolmankhanehFractional calculus is a branch of classical mathematics, which deals with the generalization of fractional order derivative and integral operator. Recently, a great deal of research has been carried out on the fractional calculus to study the phenomena associated with MoreFractional calculus is a branch of classical mathematics, which deals with the generalization of fractional order derivative and integral operator. Recently, a great deal of research has been carried out on the fractional calculus to study the phenomena associated with fractal structures and processes. Fractals have a fractional dimension and occur naturally in non-linear and imbalanced phenomena in various forms and contexts. In recent years, various types of derivatives and fractional and fractal calculus have been proposed by many scientists and have been extensively utilized. Measurements are localized in physical processes, and local fractional calculus is a useful tool for solving some type of physical and engineering problems. Gangal studied the local fractional calculus and got the relation between it and the fractals. Using the local fractional calculus and fractal properties, he defined the fractal-alpha calculus on a subset of the real line, which is a simple calculs, useful, structural and algorithmic. In this study, we first describe the fractal-F alpha calculus. Next, we propose The generalized variational iteration method based on the fractal calculus. To show the efficiency of fractal calculus and the new method, we solve several fractal partial differential equations with this method and show that this method is better, easier and more suitable than the two other methods mention the above. Manuscript profile -
Open Access Article
7 - New operational matrix for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative
M. alipour P. allahgholiIn this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of pro MoreIn this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractional derivative, which has not been undertaken before. By using the function approximations based on the Bernstein basis and mentioned operational matrices, the optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative is reduced to a system of algebraic equations that easily solvable by Newton’s iteration method. We apply the proposed method for solving two examples. The numerical results show that present method is simple in implementation and the approximate solutions are in high accuracy. Some comparisons with other method guarantee that the results are reasonable. Also, the obtained solutions approach to classical solutions as the order of the fractional derivatives approach to 1, as expected. Manuscript profile -
Open Access Article
8 - Option Hedging in Jump-Diffusion Markets by Malliavin Calculus
Minoo Bakhsh Mohammadlou Rahman FarnooshWe obtain the hedging strategy in a jump-diffusion market by minimizing the variance of the residual risk. We calculate the residual risk by two formulas: the Ito's formula and the jump-diffusion version of the Clark-Ocone formula. The results show that Malliavin calcul MoreWe obtain the hedging strategy in a jump-diffusion market by minimizing the variance of the residual risk. We calculate the residual risk by two formulas: the Ito's formula and the jump-diffusion version of the Clark-Ocone formula. The results show that Malliavin calculus can generate the hedging strategy under weaker assumptions. Thus afterward we do not require to check the strong condition on and the condition with bounded derivative is sufficient. Manuscript profile -
Open Access Article
9 - روش عددی صریح برای سیستمهای دینامیک غیرموضعی با تأخیردر زمان بر پایه درونیابی اسپلاین مربعی
حسن پنج مینی بهروز پارسا مقدم الهام هاشمی زادهدر این مقاله، روشی صریح برای حل عددی معادلات دیفرانسیل غیرموضعی با تأخیر در زمان ارائه و مورد بررسی قرار می گیرد. در روش ارائه شده، درونیابی اسپلاین مربعی بکار گرفته شده است و خطای روش ارائه شده آنالیز گردیده است. کارایی و اعتبار روش پیشنهادی در مدلهای آیکدا و هاتچینسو Moreدر این مقاله، روشی صریح برای حل عددی معادلات دیفرانسیل غیرموضعی با تأخیر در زمان ارائه و مورد بررسی قرار می گیرد. در روش ارائه شده، درونیابی اسپلاین مربعی بکار گرفته شده است و خطای روش ارائه شده آنالیز گردیده است. کارایی و اعتبار روش پیشنهادی در مدلهای آیکدا و هاتچینسون غیرموضعی تأخیری با استناد مفاهیم خطا و همگرایی روشهای عددی به ازای مقادیر مختلف پارامترهای مرتبه کسری نمایان شده است. Manuscript profile -
Open Access Article
10 - Application of Variational Calculus to Integrability of Differential Equations with Physical Applications
Mehmet Pakdemirli -
Open Access Article
11 - Fractional Cattaneo Heat Equation in a Multilayer Elliptic Ring Membrane and its Thermal Stresses
G Dhameja L Khalsa V VargheseA fractional Cattaneo model from the generalized Cattaneo model with two fractional derivatives of different orders is considered for studying the thermoelastic response for a multilayer elliptic ring membrane with source function. The solution is obtained by applying a MoreA fractional Cattaneo model from the generalized Cattaneo model with two fractional derivatives of different orders is considered for studying the thermoelastic response for a multilayer elliptic ring membrane with source function. The solution is obtained by applying an integral transform technique analogous to Vodicka's approach considering series expansion functions in terms of an eigenfunction to the generalized fractional Cattaneo-type heat conduction equation within an elliptic coordinates system. The analytical expressions of displacement and stress components employing Airy's stress function approach are investigated. The results are obtained as a series solution in terms of Mathieu functions and hold convergence test. The effects of fractional parameters on the temperature fields and their thermal stresses are also discussed. The findings are depicted graphically for different kinds of surface temperature gradients, and it is distinguished that the higher the fractional-order parameter, the higher the thermal response. Lastly, the generalized theory of thermoelasticity predicts an instantaneous response, but the fractional theory, which is currently under consideration, predicts a delayed response to physical stimuli, which is something that can be seen occurring in nature. This delayed response can be explained by the fact that fractional theories are currently being considered. This gives credibility to the motivation behind this topic of study in the research. Manuscript profile -
Open Access Article
12 - Application of Mathematics in Financial Management
Sanjay Tripathi -
Open Access Article
13 - On a Generalized Subclass of p-Valent Meromorphic Functions by Defined q-Derivative Operator
Mohammad Hassan Golmohammadi Shahram Najafzadeh Mohammad Reza Forutan -
Open Access Article
14 - An anticipating class of Fuzzy Stochastic Differential Equations
Hossein Jafari Hamed Farahani Mahmoud Paripour -
Open Access Article
15 - A General Method for Designing Fractional Order PID Controller
Marzieh Safaei Saeed Hosseinia Mojtaba Hosseini ToodeshkiThe idea of using fractional order calculus in control became apparent when this kind of calculus was accepted as a powerful tool in many applications. This resulted in a new generation of PID controller called fractional order PID Controller, named as Controller. MoreThe idea of using fractional order calculus in control became apparent when this kind of calculus was accepted as a powerful tool in many applications. This resulted in a new generation of PID controller called fractional order PID Controller, named as Controller. controller is more flexible and provides a better response with larger stability region as compared with standard PID controller. This paper presents a simple and reliable method for finding the family of controllers. The required calculations are done in frequency domain based on frequency response of the system and the stability region is specified in the parameters space. This method can be used for time-delay systems and, more generally, for any system with no transfer function. Manuscript profile -
Open Access Article
16 - Upper Bound for Queue length in Regulated Burst Service Scheduling
Mahmood Daneshvar Farzanega Hossein SaeediQuality of Service (QoS) provisioning is very important in next computer/communication networks because of increasing multimedia services. Hence, very investigations are performed in this area. Scheduling algorithms effect QoS provisioning. Lately, a scheduling algorith MoreQuality of Service (QoS) provisioning is very important in next computer/communication networks because of increasing multimedia services. Hence, very investigations are performed in this area. Scheduling algorithms effect QoS provisioning. Lately, a scheduling algorithm called Regulated Burst Service Scheduling (RBSS) suggested by author in [1] to provide a better service to bursty and delay sensitive services such as video. One of the most significant feature in RBSS is considering burstiness of arrival traffic in scheduling algorithm. In this paper, an upper bound of queue length or buffer size and service curve are calculated by Network Calculus analysis for RBSS. Because in RBSS queue length is a parameter that is considered in scheduling arbitrator, analysis results a differential inequality to obtain service curve. To simplify, arrival traffic is assumed to be linear that is defined in the paper clearly. This paper help to analysis delay in RBSS for different traffic with different specifications. Therefore, QoS provisioning will be evaluated. Manuscript profile -
Open Access Article
17 - Application of DJ method to Ito stochastic differential equations
H. Deilami Azodi -
Open Access Article
18 - Airy equation with memory involvement via Liouville differential operator
Bahram Agheli Abdolali Neamaty Mehdi Nategh Dumitru Baleanu -
Open Access Article
19 - Some Integral Inequalities of Hermite-Hadamard Type for Multiplicatively s-Preinvex Functions
Serap Özcan -
Open Access Article
20 - NON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS
Reza Jalilian J. Rashidinia K. Farjian H. Jalilian -
Open Access Article
21 - SLIDING MODE CONTROL BASED ON FRACTIONAL ORDER CALCULUS FOR DC-DC CONVERTERS
Noureddine Bouarroudj D. Boukhetala B. Benlahbib B. Batoun -
Open Access Article
22 - Convergence of collocation Bernoulli wavelet method in solving nonlinear Fredholm integro-differential equations of fractional order
Abdolali Rooholahi Saeed AkhavanWe provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional MoreWe provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional integration is obtained and used. It works particularly well for technical applications. The convergence of the suggested strategy is the most crucial aspect to note here. The collocation approach for this issue has a unique approximation since these requirements can be shown using mathematical principles and matrices theory. Finally, some pertinent examples for which the exact solution is known are used in numerical simulation to confirm the effectiveness and relevance. Alternatively, these examples will demonstrate the viability and correctness of the suggested approach. We provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional integration is obtained and used. It works particularly well for technical applications. The convergence of the suggested strategy is the most crucial aspect to note here. The collocation approach for this issue has a unique approximation since these requirements can be shown using mathematical principles and matrices theory. Finally, some pertinent examples for which the exact solution is known are used in numerical simulation to confirm the effectiveness and relevance. Alternatively, these examples will demonstrate the viability and correctness of the suggested approach. Manuscript profile
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