Al-Fatih journal

Car following theory is a model for the motion of a number of individual vehicles as they proceed down along straight road with no passing allowed. Many mechanical physiological aspects of the deriver-vehicle-road systems make modeling difficult. However we can assume that we have a line of n perfect derivers, in the sense that each driver can follow eaxactly the low of motion which pertinent.
Now assume the position of vehicle j at time t is given by , see figure(1) below







Fig(1) Position of the Vehicles
A good rule of thumb for following another vehicle at a safe distance is allowing you the length of a car for ten meter per hour (14.67) m/s.
When we are travelling in terms of function , we have
1.A
Where =length of the car (normaly of 15 feet) and =speed of jth vehicle.
Length of a vehicle, must be added to the separation between vehicles to give the spacing

We assume that each driver is able to follow (1.A) at each time t.
This means that the driver must accelerate (or decelerate) his vehicle according to

Brave New World is a dystopian novel by Aldous Huxley(1894-1963) , first published in 1932 . Set in London in "the year" 2540 . The novel anticipates developments in reproductive technology , biological engineering , and sleep-learning that combine to change society . People all around the world are part of a totalitarian state , free from war , hatred , poverty , disease , and pain . They enjoy leisure time , material wealth , and physical pleasure .In it , the author questions the value of 1931 London using satire and irony to portray a futuristic world in which many of the contemporary trends in British and American societies have been taken to extremes .
Actually , Huxley meant to write a satirical and fictional novel , but it turned out to be a scientific prophecy . He wanted to warn the former (his contemporary) society of the danger of scientific progress , or progress in general . The danger occurs when the weapons , media and industry , science and technology play a crucial role . The main thrust of science and technology thus has served oppressors and hindered the expansion of peace and freedom .
Huxley’s analysis of society and science can be traced back to one guiding principle that was taken from the famous historian Lord Acton (1834-1902) and his writing about the corruption of power : that power is corrupting and absolute power corrupts absolutely . If power is corrupting , then all technologies and social arrangements that allow concentrations of power should be resisted . The abuse of power and violence are the surest way to reach corruption in which mass production depends on them mainly in Huxley’s novel .Thus, he believes that nonviolence is the only hopeful way .

Fractional calculus is an old and new branch of mathematics with a long history. It’s early beginning was in 1695 when G. W. Leibniz wrote a letter from Hanover, Germany, September 30, 1695 to G. A. L’Hopital said that which is an apparent paradox and this was found in volume 2, pp.301-302, Olms Verlag, Hildesheim, Germany 1962 and first published in 1849. After two years Leibinz wrote a letter to Wallis to discuss infinite product of and in this letter Leibinz mentioned to differential calculus and used to derivative of order . For most details of historical background see [1,5].
The first application of fractional calculus is due to Abel in 1823 in solving an integral equation which arises in the tautochrone problem which is sometimes called isochrone problem and it is of finding the shape of a fractionless wire lying in a vertical plane such that the time of slide of a bead placed on the wire slides to the lowest point of the wire in the same time regardless of where the bead is placed.

Stream of consciousness' is a narrative technique in non dramatic fiction intended to render the flow of myriad impressions-visual, auditory, physical, associative, and subliminal-that impinge on the consciousness of an individual and form part of his awareness along with the trend of his rational thoughts." ( Burkdall , p. 24 )

This term was first used by the psychologist William James in The Principles of Psychology (1890). James was formulating a psychological theory where he had discovered that " memories, thoughts and feelings exist outside the primary consciousness appear to one, not as a chain, but as a stream , a flow ." (P.11)

In his introduction on the use of this narrative technique, Robert Hurley shows that It was first used, as a literary term, in the late 19th century. This term is " employed to evince subjective as well as objective reality. It reveals the character's feelings, thoughts, and actions, often following an associative rather than a logical sequence, without commentary by the author. Widely used in narrative fiction, the technique was perhaps brought to its highest point of development in early twentieth century novels where stream of consciousness plays an important role"
(Hurley, p.19 ) .

As far as the development of the English novel in the 20th century is concerned , John J. Richetti states that "some novelists attempted in their distinctive works to capture the total flow of their characters' consciousness, rather than limit themselves to rational thoughts. To represent the full richness, speed, and subtlety of the mind at work, the writer incorporates snatches of incoherent thought, ungrammatical constructions, and free association of ideas, images, and words at the pre- speech level .Amongst these works were ;William Faulkner's The Sound and the Fury (1929) , Virginia Woolf's The waves (1931) , and James Joyce's Ulysses (1922) and A Portrait of the Artist as a Young man (1916)." ( Richetti, p. 36 ) . He also adds : " Novelists of the early and mid-20th century had contributed greatly to modern literature by abandoning traditional narrative style and pioneering the use of stream of consciousness. The British writer Dorothy Richardson is considered by some actually to be the pioneer in use of the device. Her novel Pilgrimage(1911-1938), a 12-volume sequence, is an intense analysis of the development of a sensitive young woman and her responses to the world around her." (p.41 ). With regard to this subject, Walter Allen explains in his essay in The English Novel in 1924 and After that :
the phrase Stream of consciousness was taken over- first , it seems , by May Sinclair, in 1918 reviewing Dorothy Richardson's novels- to denote the new method of rendering consciousness itself as it follows from moment to moment, a method used with varying degrees of intensity by Dorothy Richardson, Joyce and Virginia Woolf , though never by Lawrence. ( p. 345)