# History

**Nigmatullin Rashid** was outstanding soviet scientist in the region of radioelectronics, creator of the scientific school, organizer of the high education and the public figure. He was the doctor of the mathematics and phys-ics (1965), full professor (1967), honored worker of science and technics of the Russian Federation (1971). He was born in Kazan. Then the service in the Soviet Army (1941-1945), the participant of the Great Patriot-ic War The graduator of the Kazan State University (KSU), the postgraduate student of the KSU (1950-1953), the Candidate of the Physics and Mathematics Sciences (1953), the reader (1953). Starting from 1953 year, he was invited to the KAI: the head of department of the theoretical radio-techniques and electronics (1954-1988), the rector of KAI КАИ (1967-1977), full professor of the department (1988-1991). The chair-man of the Supreme Council of the TASSR (1971-1980). He was decorated by the Lenin’s Order, of the Labor Red Banner, the Honored golden and silver barges and medals of the All Union Exhibition of the USSR.

The scientific activity of the R. Sh. Nigmatullin was concentrated in the laboratories of the Radioelectron-ics and Informative-Measurement Technics department of the KNRTU-KAI and started from 1953 year from the moments of the creation of this department in KAI.

In the first time, the R. Sh. Nigmatullin was realized the operations of the fractional differentiation and integra-tion in the beginning of the 60-s of the last century. For realization of this idea he used electrochemical ele-ments, later he developed the methods of the synthesis of these element using the poly-chain RLC elements that enabled to realize these specific operations in real devices.

In the frame of his scientific school, there were devel-oped mathematical and radioelectronics applications of the fractional operators in the different branches of science and techniques. Under his direct supervision the joint (together with the RAS) the research laborato-ry corresponding to this direction of the research was created (1974-1991).

The scientists of the Nigmatullin’s school published more 900 papers, received 160 patents and authorship certificates, they suggested for industry more than 240 original devices.

Now the School has wide scientific connections with scientific structures of Russia and abroad. In particu-lar, with the leading scientists and organizations from France, China, Germany, Italy, Bulgaria and Serbia.

**Rashid Sh. Nigmatullin** was born in 1923 in Kazan, Russia Federation (then Soviet Union). He was the Rector (1967-1977) of the Kazan Aviation Institute, and it was during his tenure that it was adopted, in 1973, the name of Andrey Nikolayevich Tupolev, a famous Russian aircraft designer (who had died in the year before). Then KAI received the official name called Kazan National Research Technical University named after A.N. Tupolev-KAI (KNRTU-KAI). As a publicly active man he was also Chairman (1971-1980) of the Supreme Council of the Tatarstan Autonomous Soviet Socialist Republic (TASSR). For many years he was the head of the Theory of RadioEngineering and Electron-ics Department (1954-1988) and had many pupils and followers (including his son Raoul, 40 Dr.Sc., 25 Ph.D., etc.). They contributed to further development of the science and its applications in the related areas. Rashid Nigmatullin died in 1991, leaving a great num-ber of scientific ideas and projects unfinished. In November 2013, KNRTU - KAI organized the Internation-al Scientific and Technical Conference called “Nig-matullin’s Readings” - a traditional event, this time dedicated to the 90th anniversary of birthday of Prof. R. Sh. Nigmatullin. See details in the Editorial Note in this journal. The basic directions of his scientific activi-ty were: molecular electronics, analysis and synthesis of electric circuits, mathematical and electric model-ling of the charge transmission on the interphase boundary electrode/electrolyte. He was working and creating new trends in the fields of radio-engineering, radioelectronics, electrochemistry and other related applicable sciences. Yet in the 1950s Prof. Nigmatullin introduced new concepts and ideas to build miniature electronic devices and detectors by using the properties of the systems at the boundary electrode/fluid, and es-tablished that in these models the fractional differential and integration operations are realized. As an electri-cal analogue of diffusion resistance, he suggested a semi-infinite resistor-capacity RC-cable, in which the process of distribution of the potential is similar to the diffusion process. Nigmatullin established that the in-put impedance of the system electrode/electrolyte is proportional to p−1/2, where p is the Laplace operator. This was a technical realization of the mathematical operations of fractional order (semi-order) integro-differentiation, that can be found in his papers pub-lished in 1964 year. He proposed a polarography method for construction of fractional-differentiated polarograms; this innovation helped to find, with enough speed and accuracy (1-2%), the form of the desired polarogram after a fractional differentiation. Another proposal that became very useful in the FC applications came from analysis of the integral equa-tion given by Nigmatullin to relate the surface concen-tration and the density of the substance flow through the electrode. He showed that differentiating by d/dt1/2 the time variance of the surface concentration C(0,t) it is possible to find directly the gradient of concentration or density, thus avoiding to solve the boundary value problem for the diffusion equation. This property be-came the base of electrical modelling of cells. In the mid-1980s, FC was related with the so-called constant phase elements (CPE) and also with the objects of the fractal geometry, thus finding new horizons for appli-cations. Nigmatullin expected that the close relation-ship exists, since any arbitrary mathematical operation has, at its physical realization, a definite geometry or topology. He thought about the representation of the diffusion impedance operator via a cascade-model of involved RC-elements. These RC elements should have a self-similar structure to be copied on the different scales. These ideas and relationships including the complex parts of the non-integer integrals and deriva-tives were developed and mathematically proved later by his son Prof. Raoul R. Nigmatullin.

*HISTORICAL SURVEY SOME PIONEERS OF THE APPLICATIONS OF FRACTIONAL CALCULUS*

*Duarte Valerio, Jose Tenreiro Machado, Virginia Kiry-akova //Fractional Calculus &Applied Analysis., V17, N2, 2014*