Related papers: Structural derivatives on time scales
Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl…
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
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…
The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the…
This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on time scales that are neither delta nor nabla differentiable can…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
In this paper, we present an overview of the development of one of the most dynamic areas of mathematics today: local differential operators of non-integer order. The underlying question is whether we are witnessing a period of…
The goal of this communication is to propose a generalized notion of the "traditional derivative". This generalization includes the fractional derivatives such as the Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
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…
By means of the shift operators we introduce a new periodicity concept on time scales. This new approach will enable researchers to investigate periodicity notion on a large class of time scales whose members may not satisfy the condition:…
There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related…