Related papers: Differentiation of the Wright functions with respe…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
In this work we show that it is possible to calculate the fractional integrals and derivatives of order $\alpha$ (using the Riemann-Liouville formulation) of power functions $\left( t-\ast\right) ^{\beta}$ with $\beta$ being any real value,…
We obtain a vector-valued subordination principle for $(g_{\alpha}, g_{\alpha})$-regularized resolvent families which unified and improves various previous results in the literature. As a consequence we establish new relations between…
Suppose that P_{\theta}(g) is a linear functional of a Dirichlet process with shape \theta H, where \theta >0 is the total mass and H is a fixed probability measure. This paper describes how one can use the well-known Bayesian prior to…
In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and…
This paper is devoted to the study of the $M$-Wright function ($M_{\alpha}(t)$) which is the inverse Laplace transform of the single-parameter Mittag-Leffler (ML) function ($E_{\alpha}(-s)$). Because $E_{\alpha}(-s)$ can be viewed as the…
Motivated from studies on anomalous diffusion, we show that the memory function $M(t)$ of complex materials, that their creep compliance follows a power law, $J(t)\sim t^q$ with $q\in \mathbb{R}^+$, is the fractional derivative of the Dirac…
This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…
In order to describe more complex problem using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with…
In this paper, we present an extension of Mittag-Leffler function by using the extension of beta functions (\"{O}zergin et al. in J. Comput. Appl. Math. 235 (2011), 4601-4610) and obtain some integral representation of this newly defined…
In this paper we extend the Zeta function regularization technique, which gives a meaningful solution to divergent power series, in order to assign finite values to divergent integral of certain transcendental functions $f(x)$. The…
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local…
We investigate the log-concavity on the half-line of the Wright function $\phi(-\alpha,\beta,-x),$ in the probabilistic setting $\alpha\in (0,1)$ and $\beta \ge 0.$ Applications are given to the construction of generalized entropies…
In this paper we introduce a new fractional derivative with respect to another function the so-called $\psi$-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
In this paper we find the partial sums of two kinds normalized Wright functions and the partial sums of Alexander transform of these normalized Wright functions.
We provide the increasing eigenfunctions associated to spectrally negative self-similar Feller semigroups, which have been introduced by Lamperti. These eigenfunctions are expressed in terms of a new family of power series which includes,…
In this paper, we begin by applying the Laplace transform to derive closed forms for several challenging integrals that seem nearly impossible to evaluate. By utilizing the solution to the Pythagorean equation $a^2 + b^2 = c^2$, these…
Some power series representations of the modified Bessel functions (McDonald functions $K_{\alpha}$) are derived using the relatively little known formalism of fractional derivatives. The resulting summation formulae are believed to be new.