using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

Making use of an extended fractional differintegral operator ( introduced recently by Patel and Mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of this subclass.

making use of an extended fractional differintegral operator ( introduced recently by patel and mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of this subclass.

Making use of an extended fractional differintegral operator (introduced recently by Patel and Mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of the subclass.

In view of the usefulness and great importance of fractional kinetic equations due to their occurrence in certain astrophysical problems, we have further investigated the generalized fractional kinetic equations; solutions of which contain the Rand Gfunctions of Lorenzo and Hartley (the generalized functions for the fractional calculus). The aim of this paper is to investigate the solutions of ...

In this paper, by applying a generalized extended fractional differintegral operator S ,μ,η 0,z (z ∈ △; p ∈ N; μ,η ∈ R; μ < p+ 1;−∞ < λ < η + p+ 1) we define a new class convex functions CV λ ,μ,η p (α;A,B) and several sharp inclusion relationships and other interesting properties were discussed by using the techniques of differential subordination.

2. Preliminaries Fractional differintegration’s set foot in control compass, also consistency of Caputo definition among the other fractional derivative’s definitions with engineering applications, is caused to devote this section to the basic definition of fractional calculus and its properties (Table 1). The Riemann–Liouville (RL) and the Caputo are the most popular fractional derivatives def...

Abstract. In the present paper, we solve three boundary value problems related to the temperature field in oil strata – the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the soluti...