In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.

In this paper, we investigate the controllability of a class impulsive ψ-Caputo fractional evolution equations Sobolev type in Banach spaces. Sufficient conditions are presented by two new characteristic solution operators, calculus, and Schauder fixed point theorem. Our works generalizations continuations recent results about equations. Finally, an example is given to illustrate effectiveness ...

An attempt is made here to study the Mittag–Leffler function with two variables. Its various properties including integral and operational relationships other known functions of one variable, pure differential recurrence relations, Euler transform, Laplace Mellin Whittaker Mellin–Barnes representation, its relationship Wright hypergeometric are investigated established. Also, variables associat...

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...

In this survey talk we aim to clarify the close relationships between the operators of the generalized fractional calculus (GFC), some classes of generalized hypergeo-metric functions and generalizations of the classical integral transforms. The GFC developed in [1] is based on the essential use of the Special Functions (SF). The generalized (multiple) fractional integrals and derivatives are d...

In this article, the problems of fractional calculus variations are discussed based on generalized operators, and corresponding Lagrange equations established. Then, Noether symmetry method perturbation to analyzed in order find integrals equations. As a result, conserved quantities adiabatic invariants obtained. Due universality results achieved here can be used solve other specific problems. ...

*Correspondence: [email protected] 2Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey 3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia Full list of author information is available at the end of the article Abstract In this paper, we investigate the...

Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse ...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

AbstractIn this paper we introduce the subclass K(μ, γ, η, α, β) of β-uniformly convex and β-uniformly starlike functions which are analytic and multivalent with negative coefficients defined by using fractional calculus operators. Characterization property exhibited by the functions in the class and the results of modified Hadamard product are discussed. Connections with the popular subclasses...