Related papers: Marichev-Saigo-Maeda fractional operator represent…

In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…

In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their…

Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…

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 paper, by using a general result on the monotonicity of quotients of power series, our aim is to prove some monotonicity and convexity results for the modified Struve functions. Moreover, as consequences of the above mentioned…

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.

In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…

There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related…

In this paper, we obtain new results related to Minkowski fractional integral inequality using generalized k-fractional integral operator which is in terms of the Gauss hypergeometric function.

The quaternionic valued functions of a quaternionic variable, often referred to as slice regular functions has been studied extensively due to the large number of generali\-zed results of the theory of one complex variable, see…

In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. The spectral radii of the fractional differential matrices…

This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…

The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is…

Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…

In this paper, we have established some generalized integral inequalities of Hermite-Hadamard-Fej\'er type for generalized fractional integrals. The results presented here would provide generalizations of those given in earlier works.

This is a survey paper in two parts. In the first part we list main variants of one-dimensional fractional integrodifferential operators. Also some historical and priority remarks are given. As a special question we consider the impact of…

This paper is devoted to the general theory of systems of time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order…

Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…

Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The…