Related papers: Generalized Fractional Derivative, Fractional diff…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of Beta function recently defined by Shadab et al.[19]. Moreover, we establish some results related to the newly…
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
In this paper, we derive certain formulas giving the Laplace transforms of two generalized fractional integral operators introduced recently in [Fract. Calc. Appl. Anal. 20 (2) (2017), 422--446]. The main results provide generalizations to…
In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair…
The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small…
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
The natural forms of the Leibniz rule for the $k$th derivative of a product and of Fa\`a di Bruno's formula for the $k$th derivative of a composition involve the differential operator $\partial^k/\partial x_1 ... \partial x_k$ rather than…
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, we are primarily concerned with the study of entire and analytical solutions of abstract degenerate (multi-term) fractional differential equations with Caputo time-fractional derivatives. We also analyze systems of such…
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
We introduce two kinds of fractional integral operators; the one is defined via the exponential-integral function $$ E_1(x)=\int_x^\infty \frac{e^{-t}}{t}\,dt,\quad x>0, $$ and the other is defined via the special function $$…
Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
Holderian functions have strong non-linearities, which result in singularities in the derivatives. This manuscript presents several fractional-order Taylor expansions of H\"olderian functions around points of non- differentiability. These…
In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…
In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…