Related papers: On Hilfer fractional difference operator

We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are…

H\"older functions represent mathematical models of nonlinear physical phenomena. This work investigates the general conditions of existence of fractional velocity as a localized generalization of ordinary derivative with regard to the…

A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…

We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…

This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate…

New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…

In this article, we obtain sufficient conditions on existence, uniqueness and Ulam--Hyers stability of solutions for a coupled system of two-point nabla fractional difference boundary value problems, using Banach fixed point theorem and…

A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…

This paper presents an algebraic approach to characterizing higher-order differential operators. While the foundational Leibniz rule addresses first-order derivatives, its extension to higher orders typically involves identities relating…

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…

The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…

We study the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied t^pf(t) instead of f(t) in these integrals and with parameter p a new class of…

The main objective of this article is to introduce Euler-Riesz difference sequence spaces of fractional order ${\tau} $ along with infinite matrices. Some topological properties of these spaces are considered here along with the Schauder…

We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…

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…

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

The fractional calculus of variations is now a subject under strong research. Different definitions for fractional derivatives and integrals are used, depending on the purpose under study. In this paper the fractional operators are defined…

The purpose of this article is to study Bohr inequalities involving the absolute values of the coefficients of an operator valued function. To be more specific, we establish an operator valued analogue of a classical result regarding the…

The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…