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Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the 'critical order' 2 − s and not so for orders between 2 − s and 1, where s, 1 < s < 2, is the box dimension of the graph of the function. This observation is consolidated in the general… (More)

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is… (More)

- Abhay Parvate, A D Gangal
- 2003

A new calculus based on fractal subsets of the real line is formulated. In this calculus, an integral of order α, 0 < α ≤ 1, called F α-integral, is defined, which is suitable to integrate functions with fractal support F of dimension α. Further, a derivative of order α, 0 < α ≤ 1, called F α-derivative, is defined, which enables us to differentiate… (More)

ii CERTIFIED that the work incorporated in the thesis Studies of fractal structures and processes using methods of the fractional calculus submitted by Shri. / Smt. Kiran M. Kolwankar was carried out by the candidate under my guidance. Such material as has been obtained from other sources has been duly acknowledged in the thesis. iii Acknowledgement I take… (More)

Weierstrass's everywhere continuous but nowhere diierentiable function is shown to be locally continuously fractionally diierentiable everywhere for all orders below thècritical order' 2?s and not so for orders between 2?s and 1, where s, 1 < s < 2, is the box dimension of the graph of the function. This observation is consolidated in the general result… (More)

Membrane proteins exhibit charge anisotropy across the bilayer with the vector positive inwards. The proton pumps, primary or secondary, which have been examined as a subset of these membrane proteins, also reveal charge anisotropy based on their sequence data. The direction of the anisotropy appears to satisfy the observed directional gradient of protons… (More)

Numerical simulations on a 2-dimensional model system showed that voids are induced primarily due to shape anisotropy in binary mixtures of interacting disks. The results of such a simple model account for the key features seen in a variety of flux experiments using liposomes and biological membranes [1].

We propose a 2-d computational model-system comprising a mixture of spheres and the objects of some other shapes, interacting via the Lennard-Jones potential. We propose a reliable and efficient numerical algorithm to obtain void statistics. The void distribution, in turn, determines the selective permeability across the system and bears a remarkable… (More)

The sets and curves of fractional dimension have been constructed and found to be useful at number of places in science [1]. They are used to model various irregular phenomena. It is wellknown that the usual calculus is inadequate to handle such structures and processes. Therefore a new calculus should be developed which incorporates fractals naturally.… (More)

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