Related papers: A new sigmoidal fractional derivative for regulari…
In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. Our approach utilizes a known characterization of the…
In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional…
In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As…
In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. It is based on…
Here we define a Caputo like discrete fractional difference and we compare it to the earlier defined Riemann-Liouville fractional discrete analog. Then we produce discrete fractional Taylor formulae for the first time, and we estimate their…
We consider a partial differential equation associated with a mathematical model describing the concentration of nutrients in blood which interferes directly on the erythrocyte sedimentation rate in the case of an average fluid velocity…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…
We derive a fundamental solution $\mathscr{E}$ to a space-fractional diffusion problem on the half-line. The equation involves the Caputo derivative. We establish properties of $\mathscr{E}$ as well as formulas for solutions to the…
With the modified Riemann-Liouville fractional derivative, a fractional Tu formula is presented to investigate generalized Hamilton structure of fractional soliton equations. The obtained results can be reduced to the classical Hamilton…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…
In this paper we present three types of Caputo-Hadamard derivatives of variable fractional order, and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is…
We formulate fractional difference equations of Riemann-Liouville and Caputo type in a functional analytical framework. Main results are existence of solutions on Hilbert space-valued weighted sequence spaces and a condition for stability…
In this work, we aim to extend the application of the fractional calculus in the realm of quantum mechanics. We present a time fractional Pauli equation containing Caputo fractional derivative. By use of the new equation we study the…
In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main…
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…
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…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…