We report on our recent breakthrough [9] in the costruction for q > 0 of Hermitean and “tractable” differential operators out of the Uqso(N)covariant differential calculus on the noncommutative manifolds Rq (the socalled “quantum Euclidean spaces”).

We report on our recent breakthrough [9] in the costruction for q > 0 of Hermitean and “tractable” differential operators out of the Uqso(N)covariant differential calculus on the noncommutative manifolds Rq (the socalled “quantum Euclidean spaces”).

Although many mathematicians have searched on the fractional calculus since many years ago, but its application in engineering, especially in modeling and control, does not have many antecedents. Since there are much freedom in choosing the order of differentiator and integrator in fractional calculus, it is possible to model the physical systems accurately. This paper deals with time-domain id...

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

Abstract At first, we recall the q -operators in context of -calculus and by examining these operators will introduce new definitions partial -operators. Then, investigate some refinements inequalities Hermite–Hadamard ( $H-H$ H − ) type on coordinated convex functions involving defined From ...

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account general form non-locality in kernels differential and integral operators. Self-consistency involves proving generalizations all fundamental theorems for generalized In the FVC from power-law nonlocality space, we use (GFC) Luchko approach, which was published 2021. This...