Related papers: Analytic computations of digamma function using so…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
In this paper, a new identity for convex functions is derived. A consequence of the identity is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in…
In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.
By making use of the identity obtained by Sarikaya, some new Hermite-Hadamard type inequalities for h-convex functions on the co-ordinates via fractional integrals are established. Our results have some relationships with the results of…
Using fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued H\"{o}lder continuous functions of order $\displaystyle \beta \in (\frac13, \frac12)$ and $f$ is a continuously…
We show that the higher derivatives of the Riemann zeta function may be expressed in terms of integrals involving the digamma function. Related integrals for the Stieltjes constants are also shown. We also present a formula for the…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
In this paper, we tackle unresolved inquiries by Ferreira et al. \cite{bruno} in their recent publication, ``Functional Identity on Division Algebras". We delve into the intricate behavior of additive functions on matrix algebras over…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
In fractional calculus there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and…
We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
The present paper plans to examine the existence, uniqueness and data dependence of the solution of the fractional functional differential equation with the abstract operator of Volterra, in the context of the Picard operators. We present…
We prove new estimates of the Caputo derivative of order $\alpha \in (0,1]$ for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on…
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…
We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…