The formulations of Riemann-Liouville and Caputo derivatives in the complex plane are presented. Two versions corresponding to the whole or half plane. It is shown that they can be obtained from the Grünwald-Letnikov derivative.

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals.

For a class of one-dimensional reaction-diffusion equations, we establish the existence of generalized fronts, as recently defined by Berestycki and Hamel. We also prove uniform nondegeneracy estimates, such as a lower bound on the time derivative on some level sets, as well as a lower bound on the spatial derivative.

A new fractional subequation method is proposed for finding exact solutions for fractional partial differential equations (FPDEs). The fractional derivative is defined in the sense ofmodified Riemann-Liouville derivative. As applications, abundant exact solutions including solitary wave solutions as well as periodic wave solutions for the space-time fractional generalized Hirota-Satsuma coupled...

The Lagrangian approach to the development of dynamics equations for a multi-body system, constrained or otherwise, requires solving the forWard kinematics of the system at velocity level in order to derive the kinetic energy of the system. The kinetic-energy expression should then be differentiated multiple times to derive the equations of motion of the system. Among these differentiations, th...

By space-fractional (or L evy-Feller) diiusion processes we mean the processes governed by a generalized diiusion equation which generates all L evy stable probability distributions with index (0 < 2), including the two symmetric most popular laws, Cauchy (= 1) and Gauss (= 2). This generalized equation is obtained from the standard linear diiusion equation by replacing the second-order space d...

Throughout this paper, let k be a field of characteristic 2. Let G be a classical group over k and g be its Lie algebra. Let g be the dual vector space of g. Fix a Borel subgroup B and a maximal torus T ⊂ B of G. Let B = TU be the Levi decomposition of B. Let b, t and n be the Lie algebra of B, T and U respectively. We have a natural action of G on g, g.ξ(x) = ξ(Ad(g)x) for g ∈ G, ξ ∈ g and x ∈...

A novel framework for single and multiple motion estimation is presented. It is based on a generalized structure tensor that contains blurred products of directional derivatives. The order of differentiation increases with the number of motions but more general linear filters can be used instead of derivatives. From the general framework, a hierarchical algorithm for motion estimation is derive...

The paper [3] started a new approach to Abstract Algebraic Logic in which, instead of the usual equivalence-based classification of logical systems leading to the well-known Leibniz hierarchy of protoalgebraic logics (see [5]), we proposed an alternative setting based on implication connectives. By studying the properties of weak p-implications (understood as generalized connectives defined by ...