Related papers: A subordination principle on Wright functions and …
We introduce a new derivative, the so-called truncated $\mathcal{V}$-fractional derivative for $\alpha$-differentiable functions through the six parameters truncated Mittag-Leffler function, which generalizes different fractional…
This paper is in concern with Cauchy problems involving the fractional derivatives with respect to another function. Results of existence, uniqueness, and Taylor series among others are established in appropriate functional spaces. We prove…
By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second…
Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several…
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…
In this note we prove some new results about the application of Wright functions of the first kind to solve fractional differential equations with variable coefficients. Then, we consider some applications of these results in order to…
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…
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…
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions $\phi(b)\in…
The main goal of this paper is to obtain sufficient conditions so that Le Roy type functions and multivariate Le Roy type functions satisfy subordination of exponential function. Moreover conditions on parameters have been derived to claim…
We consider a class of two-dimensional functions f(x,y) with the property that the smallness of its rectangular norm implies the smallness of rectangular norm for f(x,x+y). Also we study a family of functions f(x,y) having a similar…
Product-to-sum identities for trigonometric functions play a fundamental role in function theory and numerous applications. In this spirit, we present convolution-to-sum identities for Mittag-Leffler type functions. Using a Laplace domain…
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 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…
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…
The convolution quadrature theory is a systematic approach to analyse the approximation of the Riemann-Liouville fractional operator $I^{\alpha}$ at node $x_{n}$. In this paper, we develop the shifted convolution quadrature ($SCQ$) theory…
In this paper, we obtain some application of first-order differential subordination, superordination and sandwich-type results involving operator for certain normalized $p$-valent analytic functions. Further, properties of $p$-valent…
The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…
We consider generalized time-fractional evolution equations of the form $$u(t)=u_0+\int_0^tk(t,s)Lu(s)ds$$ with a fairly general memory kernel $k$ and an operator $L$ being the generator of a strongly continuous semigroup. In particular,…