in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.

Fractional curl operator has been used to derive solutions to the Maxwell equations for fractional rectangular cavity resonator. These solutions to the Maxwell equations may be regarded as fractional dual solutions. Behavior of field lines and surface current density in fractional cavity resonator have been investigated with respect to the fractional parameter. Fractional parameter describes th...

Recently, optical interpretations of the fractional-Fourier-transform operator have been introduced. On the basis of this operator the fractional correlation operator is defined in two different ways that are both consistent with the definition of conventional correlation. Fractional correlation is not always a shift-invariant operation. This property leads to some new applications for fraction...

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...

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

It is well known that the complex step method is a tool that calculates derivatives by imposing a complex step in a strict sense. We extended the method by employing the fractional calculus differential operator in this paper. The fractional calculus can be taken in the sense of the Caputo operator, Riemann-Liouville operator, and so forth. Furthermore, we derived several approximations for com...

Recently, an extended operator of fractional derivative related to a generalized Beta function was used in order to obtain some generating relations involving the extended hypergeometric functions [1]. The main object of this paper is to present a further generalization of the extended fractional derivative operator and apply the generalized extended fractional derivative operator to derive lin...

The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann-Liouville fractional integration operator has been obtained.

The sub-title of this presentation could be “The fractional order integrator approach”. Although fractional order differentiation is commonly considered as the basis of fractional calculus, its effective basis is in fact fractional order integration, mainly because definitions, calculation and properties of fractional derivatives and Fractional Differential Systems (FDS) rely deeply on fraction...