In this paper, fractal calculus, which is called Fα-calculus, reviewed. Fractal calculus implemented on interpolation functions and Weierstrass functions, may be non-differentiable non-integrable in the sense of ordinary calculus. Graphical representations are presented.

By analogy with complex K–theory and reality, there are theories of unitary functor calculus both which generalisations Weiss' orthogonal calculus. In this paper we show that can be completely recovered from the in to how topological is reality via forgetting C2–action.

A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...

the computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. in this approach, a truncated hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. two illustrative examples are included todemon...

omotopy analysis method (HAM) is a promising method for handling func-tional equations. Recent publications proved the eectiveness of HAM in solvingwide variety of problems in dierent elds. HAM has a unique property whichmakes it superior to other analytic methods, this property is its ability to con-trol the convergence region of the solution series. In this work, we claried theadvantages and ...

Abstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar functions are presented. In addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

machines and sharing.Our presentation of a explicit substitution cal-culus has been driven by the correspondence withthe semantics. Of the calculi discussed above, theoriginal -calculus of Abadi et al. [1] is the onlyone with a closer correspondence to a categoricalsemantics. We see our calculus as a direct improve-ment of theirs. Moreover, in earlier work [14] Ritte...

This thesis is concerned with the formal veri cation of statecharts. Statecharts area synchronous formalism for the speci cation of reactive systems that is obtainedby introducing in classical state-transition diagrams notions of hierarchy, parallelismand communication. Propositional -calculus is a very convenient formalism for ex-pressing the properties characterizing the c...

Does the asymptotic variance of maximum composite likelihood estimator a parameter interest always decrease when nuisance parameters are known? Will necessarily become more efficient by incorporating addi- tional independent component likelihoods, or using likelihoods with higher dimension? In this note we show through illustrative examples that an- swer to both questions is no, and indeed oppo...