Related papers: On the Laguerre fractional integro-differentiation
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the…
We establish a new natural extension of Mittag-Leffler function with three variables which is so called "trivariate Mittag-Leffler function". The trivariate Mittag-Leffler function can be expressed via complex integral representation by…
In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.
In this paper, the incomplete Pochhammer ratios are defined in terms of the incomplete beta function $B_{y}(x,z)$. With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric and Appell's…
We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional…
In this article, we introduce incomplete Lauricella matrix functions (ILMFs) of $n$ variables through application of the incomplete Pochhammer matrix symbols. Furthermore there is derivation of certain properties; matrix differential…
For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for…
We Investigate two types of dual identities for Caputo fractional differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We define and characterize ultradifferentiable functions and their corresponding ultradistributions on $\RR^d_+$ using iterates of the Laguerre operator. The characterization is based on decay or growth conditions of the coefficients in…
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…
The integral representation of the Hadamard product of two functions is used to prove several Euler-type series transformation formulas. As applications we obtain three binomial identities involving harmonic numbers and an identity for the…
In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The…
Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel…
It is well-known that one-dimensional time fractional diffusion-wave equations with variable coefficients can be reduced to ordinary fractional differential equations and systems of linear fractional differential equations via scaling…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…
The six-vertex model with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is obtained. The kernel of the corrtesponding integral operator depends on Laguerre…
In this paper, we state with a variational method a general theorem providing the existence of a weak solution $u$ for fractional Euler-Lagrange equations of the type: $$ \dfrac{\partial L}{\partial x} (u,D^\alpha_- u,t) + D^\alpha_+…