fuzzy fractional differential equations with the generalized atangana baleanu fractional derivative abstract in this paper we introduce a generalization of atangana baleanu type fractional calculus with respect to the generalized mittag leffler kernel which has been named as the generalized atangana baleanu gab type fractional calculus existence and uniqueness results for the initial value problems of fuzzy differential equations involving a gab fractional derivative in the caputo sense are established by employing the method of successive approximation and by means of fixed point theorems to visualize the theoretical results some examples and numerical simulations are given

a survey on fuzzy fractional variational problems abstract this paper focuses on introducing and studying generalized fuzzy euler lagrange equation and fuzzy isoperimetric problem according to the concept of caputo type fuzzy fractional derivative in the sense of the generalized fuzzy differentiability we extend and establish some definitions on fuzzy fractional calculus of variation and provide some necessary conditions to obtain the fuzzy fractional euler lagrange equation for both constrained and unconstrained fuzzy fractional variational problems the fuzzy isoperimetric problem is also investigated in relation to the generalized fuzzy euler lagrange finally two examples are given to describe the proposed approach

existence results for extremal solutions of interval fractional functional integro differential equations abstract in this study we introduce interval fractional functional integro differential equations iffides under the caputo generalized hukuhara fractional differentiability we establish some necessary comparison results and use the monotone iterative technique combined with the method of upper and lower solutions to investigate the existence of extremal solutions for iffides an example is presented to illustrate the results

fuzzy fractional functional integral and differential equations this paper is devoted to considering the existence and uniqueness results for fuzzy fractional functional integral equations employing the contraction principle moreover the approach is followed to prove the existence and uniqueness of solutions for the fuzzy fractional functional initial value problem under caputo type fuzzy fractional derivatives finally the solution to fuzzy fractional functional initial value problem under caputo type fuzzy fractional derivatives by a modified fractional euler method mfem is presented the method is illustrated by solving some examples

on detecting edges in speckle imagery methods for detecting sustained intensity changes in images corrupted by speckle are analyzed the problem is complicated by the nature of the speckle which is characterized by a high degree of correlation and approximately multiplicative signal dependence these characteristics make the automated extraction of edges in speckle very difficult for applications requiring the location and identifications of objects e g synthetic aperture radar in particular the laplacian of a gaussian log edge detector for this problem is analyzed while the log is found to be effective for detecting meaningful edges use of the log also gives rise to numerous extraneous edges having no physical correlate to alleviate these effects a ratio of averages edge detector is used in conjunction with the log the combined scheme is found to be much more effective than either of the individual edge detectors actual seasat synthetic aperture radar sar images are used to demonstrate the effectiveness of each technique

mechanics with fractional derivatives lagrangian and hamiltonian mechanics can be formulated to include derivatives of fractional order f riewe phys rev 53 1890 1996 lagrangians with fractional derivatives lead directly to equations of motion with nonconservative classical forces such as friction the present work continues the development of fractional derivative mechanics by deriving a modified hamilton s principle introducing two types of canonical transformations and deriving the hamilton jacobi equation using generalized mechanics with fractional and higher order derivatives the method is illustrated with a frictional force proportional to velocity in contrast to conventional mechanics with integer order derivatives quantization of a fractional derivative hamiltonian cannot generally be achieved by the traditional replacement of momenta with coordinate derivatives instead a quantum mechanical wave equation is proposed that follows from the hamilton jacobi equation by application of the correspondence principle

on the solution of fuzzy fractional optimal control problems with the caputo derivative abstract this paper presents an extension to fractional optimal control problems with ambiguity as the ambiguity is modeled with fuzzy method we encounter with a fuzzy fractional optimal control problem the objective in fuzzy fractional optimal control problem is to determine the best possible fuzzy control which satisfies the related fuzzy fractional dynamic systems and minimizes the fuzzy performance index here the fractional derivative is described in the caputo sense to find the solution first we state some definitions and prove some required theorems then we employ the obtained result to determine the necessary conditions furthermore we show that the obtained necessary optimality conditions become sufficient by considering some extra assumptions finally some examples are presented for more illustration of the subject

speckle reducing anisotropic diffusion this paper provides the derivation of speckle reducing anisotropic diffusion srad a diffusion method tailored to ultrasonic and radar imaging applications srad is the edge sensitive diffusion for speckled images in the same way that conventional anisotropic diffusion is the edge sensitive diffusion for images corrupted with additive noise we first show that the lee and frost filters can be cast as partial differential equations and then we derive srad by allowing edge sensitive anisotropic diffusion within this context just as the lee 1980 1981 1986 and frost 1982 filters utilize the coefficient of variation in adaptive filtering srad exploits the instantaneous coefficient of variation which is shown to be a function of the local gradient magnitude and laplacian operators we validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery we also demonstrate the algorithm performance with real sar data the performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes in the presence of speckle noise speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation variance reduction and edge localization

fuzzy fractional differential equations under caputo katugampola fractional derivative approach abstract in this work an initial value problem of caputo katugampola ck fractional differential equations in fuzzy setting is considered and an idea of successive approximations under generalized lipschitz condition is used to prove the existence and uniqueness results of the solution to the given problem in order to obtain the above results some necessary comparison theorems in real valued differential equation under ck fractional derivative are established finally a new technique to find analytical solutions of ck fuzzy fractional differential equations by using the solutions of fuzzy integer order differential equations is proposed some examples illustrating the applications of our results are presented

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

neutral fuzzy fractional functional differential equations abstract in this paper a class of fuzzy fractional functional differential equations of neutral type is investigated the existence uniqueness and iterative formula in the case of linear equations are obtained meanwhile the continuous dependence of solutions on initial data parameters and functions involved in right hand side of equation is also discussed several examples are given to illustrate the applications of our results

edge detection in ultrasound imagery using the instantaneous coefficient of variation the instantaneous coefficient of variation icov edge detector based on normalized gradient and laplacian operators has been proposed for edge detection in ultrasound images in this paper the edge detection and localization performance of the icov squared icovs detector are examined first a simplified version of the icovs detector the normalized gradient magnitude squared is scrutinized in order to reveal the statistical performance of edge detection and localization in speckled ultrasound imagery both the probability of detection and the probability of false alarm are evaluated for the detector edge localization is characterized by the position of the peak and the 3 db width of the detector response then the speckle edge response of the icovs as applied to a realistic edge model is studied through theoretical analysis we reveal the compensatory effects of the normalized laplacian operator in the icov edge detector for edge localization error an icov based edge detection algorithm is implemented in which the icov detector is embedded in a diffusion coefficient in an anisotropic diffusion process experiments with real ultrasound images have shown that the proposed algorithm is effective in extracting edges in the presence of speckle quantitatively the icovs provides a lower localization error and qualitatively a dramatic improvement in edge detection performance over an existing edge detection method for speckled imagery

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

hyers ulam stability of fuzzy fractional volterra integral equations with the kernel ψ function via successive approximation method abstract in this paper we investigative the hyers ulam stability and the hyers ulam rassias stability of fuzzy fractional volterra integral equations ffvies involving the kernel function we propose conditions for the existence uniqueness and stability of ffvie by employing the method of successive approximation to visualize the theoretical results some examples and numerical simulations are given

analysis and numerical approximation of tempered fractional calculus of variations problems abstract in this paper we study variational problems where the cost functional involves the tempered caputo fractional derivative several important optimization conditions are derived to find the optimal solution sufficient and necessary conditions are presented for different variational problems for example the cases of integral isoperimetric problem and holonomic constraints are considered as well as problems with high order derivatives a numerical scheme is proposed to determine approximations of the solution and it is illustrated through some examples

necessary optimality conditions for fuzzy variational problems the main aims of this study are to derive the fuzzy euler lagrange conditions for both fuzzy unconstrained and constrained variational problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right hand functions of its a level sets

predicting monthly streamflow using data driven models coupled with data preprocessing techniques 1 in this paper the accuracy performance of monthly streamflow forecasts is discussed when using data driven modeling techniques on the streamflow series a crisp distributed support vectors regression cdsvr model was proposed for monthly streamflow prediction in comparison with four other models autoregressive moving average arma k nearest neighbors knn artificial neural networks anns and crisp distributed artificial neural networks cdann with respect to distributed models of cdsvr and cdann the fuzzy c means fcm clustering technique first split the flow data into three subsets low medium and high levels according to the magnitudes of the data and then three single svrs or anns were fitted to three subsets this paper gives a detailed analysis on reconstruction of dynamics that was used to identify the configuration of all models except for arma to improve the model performance the data preprocessing techniques of singular spectrum analysis ssa and or moving average ma were coupled with all five models some discussions were presented 1 on the number of neighbors in knn 2 on the configuration of ann and 3 on the investigation of effects of ma and ssa two streamflow series from different locations in china xiangjiaba and danjiangkou were applied for the analysis of forecasting forecasts were conducted at four different horizons 1 3 6 and 1 2 month ahead forecasts the results showed that models fed by preprocessed data performed better than models fed by original data and cdsvr outperformed other models except for at a 6 month ahead horizon for danjiangkou for the perspective of streamflow series the ssa exhibited better effects on danjingkou data because its raw discharge series was more complex than the discharge of xiangjiaba the ma considerably improved the performance of ann cdann and cdsvr by adjusting the correlation relationship between input components and output of models it was also found that the performance of cdsvr deteriorated with the increase of the forecast horizon

a new image thresholding method based on gaussian mixture model in this paper an efficient approach to search for the global threshold of image using gaussian mixture model is proposed firstly a gray level histogram of an image is represented as a function of the frequencies of gray level then to fit the gaussian mixtures to the histogram of image the expectation maximization em algorithm is developed to estimate the number of gaussian mixture of such histograms and their corresponding parameterization finally the optimal threshold which is the average of these gaussian mixture means is chosen and the experimental results show that the new algorithm performs better

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

a survey on the initial value problems of fuzzy implicit fractional differential equations abstract the purpose of this paper is to present some basic theories of various classes of initial value problems of implicit fractional differential equation involving the caputo fuzzy type riemann liouville fuzzy type and hadamard fuzzy type concepts of fractional derivative in the case of the order 0 1 in particular the existence and uniqueness results of solution for the given initial value problems of implicit fractional differential equations is investigated in addition some results concerning continuous dependence of solutions on perturbations of the given parameters namely of the initial conditions of the function and parameters on the right hand side of the order of fractional derivative are analyzed finally some examples are given to illustrate our main results

the solvability of fuzzy fractional partial differential equations under caputo gh differentiability the foundation of the concepts of fuzzy fractional integral and caputo gh partial for fuzzy valued multivariable functions is defined as a result fuzzy fractional partial differential equations are considered and the appropriateness of local boundary value problems for hyperbolic equations is proved we present two new results on the existence of two kinds of gh weak solutions of these problems the first result is based on the banach fixed point theorem with the lipschitz condition of functions on the right hand side of equations the second result is based on the nonlinear alternative of the schauder type for fuzzy valued continuous functions without the lipschitz condition moreover we indicate the boundedness and continuous dependence of solutions on the initial data of the problems our models are embedded in the sense of caputo gh differentiability some examples are presented to illustrate the results

robust techniques for edge detection in multiplicative weibull image noise abstract recent studies of the approximately multiplicative noise present in images from coherent radar systems suggest that the first order statistics can be broadly modeled by the two parameter weibull probability density function w y y 1 exp y this paper defines and compares some novel techniques for the robust detection of sustained image irradiance changes or edges in images immersed in multiplicative weibull noise it is shown that edge detection in multiplicative noise is accomplished effectively by comparing ratios of locally adjacent image irradiance estimates to an appropriate threshold several such estimates are considered local irradiance averages optimal single order statistics and best linear unbiased estimates using order statistics the results of a statistical monte carlo performance analysis suggest that edge detection using ratios of single order statistics ros detector offers the best compromise among computational convenience edge localization and robust performance while the ratio of blues detector rob detector yields the best overall statistical and empirical noise suppression the ratio of averages detector roa detector while statistically optimal in some cases often yields inferior edge localization relative to the other schemes images corrupted by synthetically generated weibull noise are used to support the analysis

nonconservative lagrangian and hamiltonian mechanics traditional lagrangian and hamiltonian mechanics cannot be used with nonconservative forces such as friction a method is proposed that uses a lagrangian containing derivatives of fractional order a direct calculation gives an euler lagrange equation of motion for nonconservative forces conjugate momenta are defined and hamilton s equations are derived using generalized classical mechanics with fractional and higher order derivatives the method is applied to the case of a classical frictional force proportional to velocity textcopyright 1996 the american physical society

on the estimation of the coefficient of variation for anisotropic diffusion speckle filtering in this paper we focus on the problem of speckle removal by means of anisotropic diffusion and specifically on the importance of the correct estimation of the statistics involved first we derive an anisotropic diffusion filter that does not depend on a linear approximation of the speckle model assumed which is the case of a previously reported filter namely srad then we focus on the problem of estimation of the coefficient of variation of both signal and noise and of noise itself our experiments indicate that neighborhoods used for parameter estimation do not need to coincide with those used in the diffusion equations then we show that as long as the estimates are good enough the filter proposed here and the srad perform fairly closely a fact that emphasizes the importance of the correct estimation of the coefficients of variation

energy distortion exponents in lossy transmission of gaussian sources over gaussian channels lossy transmission of gaussian sources over energy limited gaussian point to point and broadcast channels is studied under the infinite bandwidth regime i e when the number of channel uses is unlimited using previously known asymptotic achievability and converse results the energy distortion exponent defined as the rate of decay of the square error distortion as the available energy to noise ratio increases without bound is completely characterized for both the point to point and broadcast channel cases turning then to the scenario of zero delay transmission where outage events with arbitrarily small probability are allowed it is shown that the same energy distortion exponent as in the infinite delay case can be achieved in all the studied scenarios

solving interval valued fractional initial value problems under caputo gh fractional differentiability abstract in this paper interval valued fractional differential equations ifdes under caputo generalized hukuhara differentiability are introduced we present existence and uniqueness results for ifdes with a krasnoselskii krein type condition the solution to interval valued fractional initial value problems under caputo type interval valued fractional derivatives by a modified fractional euler method mfem and a modified adams bashforth moulton method mabmm is also presented

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

the improper fuzzy riemann integral and its numerical integration abstract the improper fuzzy riemann integral and its numerical integration are proposed in this paper under the setting of the improper fuzzy riemann integral we can find the expectation of fuzzy random variable the level set of the improper fuzzy riemann integral is a closed interval whose end points are the improper riemann integrals thus we provide a numerical method to approximate the improper fuzzy riemann integral by invoking the simpson s rule we also fit the end points closed interval of the level set of the improper fuzzy riemann integral as polynomials with variable in a least squares sense finally the membership function of the improper fuzzy riemann integral can be transformed into nonlinear programming problem and be solved by any presented optimizer