Related papers: Fuzzification of Fractal Calculus
There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…
In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a second $\alpha$-order fractal differential equation with constant coefficients across different scenarios. We…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
There are many resources useful for processing images, most of them freely available and quite friendly to use. In spite of this abundance of tools, a study of the processing methods is still worthy of efforts. Here, we want to discuss the…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…
Fault tree analysis is a vital method of assessing safety risks. It helps to identify potential causes of accidents, assess their likelihood and severity, and suggest preventive measures. Quantitative analysis of fault trees is often done…
The calculus of finite differences is a solid foundation for the development of operations such as the derivative and the integral for infinite sequences. Here we showed a way to extend it for finite sequences. We could then define…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
In this paper, we introduce the notion of fuzzy soft numbers. Here defined fuzzy soft number and four arithmetic operations $ \tilde{+}, \tilde{-}, \tilde{\times}, \tilde{\div} $ and related properties. Also introduce Hausdorff distance,…
We investigate some basic applications of Fractional Calculus (FC) to Newtonian mechanics. After a brief review of FC, we consider a possible generalization of Newton's second law of motion and apply it to the case of a body subject to a…
Starting from a recent result expressing the Lerch zeta function as a fractional derivative, we consider further fractional derivatives of the Lerch zeta function with respect to different variables. We establish a partial differential…
Fuzzy set theory opens new vistas in computability theory and here I show this by defining a new computational metaphor--the fuzzy chemical metaphor. This metaphor is an extension of the chemical metaphor. In particular, I introduce the…
The concept of fuzzy cardinal semantic transformation as a basis for creating fuzzy semantic numeration systems is introduced in this work. Both fuzziness of the initial data - cardinals of abstract entities - and fuzziness of the…