Differential Subordinations for Fractional- Linear Transformations

Some Applications of the Principle of Differential Subordination

By applying the principle of differential subordination between analytic functions to a substantially general family of linear transformations, we derive an extension of the Briot-Bouquet differential subordination relations given in the monograph on the subject by Miller and Mocanu [8]. We also present a systematic discussion of various other linear transformations associated with differential...

On Differential Subordinations of Multivalent Functions Involving a Certain Fractional Derivative Operator

Exact solutions of a linear fractional partial differential equation via characteristics method

‎In recent years‎, ‎many methods have been studied for solving differential equations of fractional order‎, ‎such as Lie group method, ‎invariant subspace method and numerical methods‎, ‎cite{6,5,7,8}‎. Among this‎, ‎the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order‎. In this paper we apply this method f...

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

Basic results on distributed order fractional hybrid differential equations with linear perturbations

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...