Numerical Solution for Solving Nonlinear Fuzzy Fractional Integral Equation by Using Approximate Method

In this paper, we discus fractional order for fuzzy non-linear integral equation . The fractional integral is consider in the sense Riemann-liouville  and establish the exists solution  of nonlinear fuzzy fractional  integral equation. Finally, Numerical  examples are given to  illustrate the results

Recent Fixed Point Techniques in Fractional Set-Valued Dynamical Systems

In this chapter, we present a recollection of fixed point theorems and their applications in fractional set-valued dynamical systems. In particular, the fractional systems are used in describing many natural phenomena and also vastly used in engineering. We consider mainly two conditions in approaching the problem. The first condition is about the cyclicity of the involved operator and this one takes place in ordinary metric spaces. In the latter case, we develop a new fundamental theorem in modular metric spaces and apply to show solvability of fractional set-valued dynamical systems

Analytical investigation of fractional differential inclusion with a nonlocal infinite-point or Riemann–Stieltjes integral boundary conditions

Here, we investigate the existence of solutions for the initial value problem of fractional-order differential inclusion containing a nonlocal infinite-point or Riemann–Stieltjes integral boundary conditions. A sufficient condition for the uniqueness of the solution is given. The continuous dependence of the solution on the set of selections and on some data is studied. At last, examples are designed to illustrate the applicability of the theoretical results

Аnalysis of energy dissipation in the impact problems of two or more bodies

Анализиран је судар два тела као и дисипација енергије укључена кроз механизам сувог трења моделираног неглатком вишевредносном функцијом и кроз деформацију вискоеластичног штапа чији модел укључује фракционе изводе. Проблем судара два тела је приказан у форми Кошијевог проблема који припада класи неглатких вишевредносних диференцијалних једначина произвољног реалног реда. Кошијев проблем је решен нумеричким поступком заснованим на Тарнеровом алгоритму. Испитано је кретање система и дисипација енергије за разне вредности улазних параметара. Показано је да се уведене методе могу применити и на проблем судара три тела.Analiziran je sudar dva tela kao i disipacija energije uključena kroz mehanizam suvog trenja modeliranog neglatkom viševrednosnom funkcijom i kroz deformaciju viskoelastičnog štapa čiji model uključuje frakcione izvode. Problem sudara dva tela je prikazan u formi Košijevog problema koji pripada klasi neglatkih viševrednosnih diferencijalnih jednačina proizvoljnog realnog reda. Košijev problem je rešen numeričkim postupkom zasnovanim na Tarnerovom algoritmu. Ispitano je kretanje sistema i disipacija energije za razne vrednosti ulaznih parametara. Pokazano je da se uvedene metode mogu primeniti i na problem sudara tri tela.Impact of two bodies was analyzed as well as energy dissipation, which was included through dry friction phenomena modelled by a set-valued function, and through deformation of a viscoelastic rod modelled by fractional derivatives. The impact problem was presented in the form of the Cauchy problem that belongs to a class of set-valued fractional differential equations. The Cauchy problem was solved by the numerical procedure based on Turner’s algorithm. Behaviour and energy dissipation of the system was investigated for different values of input parameters. It was shown that suggested procedure can be applied on the problem of impact of three bodies

Immobilization of lead and chromium by fly ash based geopolymers.

Геополимери су синтетисани алкалном активацијом електрофилтерског пепела (ЕФП), коришћењем раствора натријум-силиката модула 1,5, при чему је извршена оптимизација услова синтезе. Оптимизација услова синтезе геополимера је подразумевала испитивање утицаја температуре (55, 80, 95 C) и времена реакције (4, 8, 16 и 24 h) на чврстоће геополимера. Утврђено је да постоји јасна корелација између карактеристика ЕФП, услова синтезе и чврстоћа геополимера. На основу вредности максималних и минималних чврстоћа при притиску геополимера извршен је избор ЕФП и одговарајућих геополимера за даље испитивање процеса имобилизације олова и хрома. Геополимер максималних чврстоћа при притиску, синтетисан је на бази ЕФП, који се показао као најреактивнији током алкалне активације, односно поседује највећи садржај честица мањих од 43 m, стакласте фазе, као и растворљивог силицијума и алуминијума у јако алкалној средини. С друге стране, геополимер минималних чврстоћа при притиску, синтетисан је на бази ЕФП који је мање реактиван, тј. поседује мањи садржај честица мањих од 43 m, стакласте фазе и растворљивог силицијума и алуминијума. Геополимери на бази изабраних полазних ЕФП представљали су референтни систем у даљим истраживањима и синтетисани су на собној температури (20 oC), а време реакције је износило 28 дана...Geopolymers were synthesized by alkali activation of fly ash (FA), using sodium silicate solution with modulus 1.5, whereby optimization of the synthesis conditions was performed. Optimization of geopolymers synthesis conditions implied the investigation of the effect of temperature (55, 80 and 95 °C) and reaction time (4, 8, 16 and 24 h) on the geopolymers strength. It was found that there was a correlation between FA characteristics, synthesis conditions, and strength of geopolymers. The selection of FA samples and corresponding geopolymers for further investigation of chromium and lead immobilization was performed based on the maximum and minimum values of the geopolymers compressive strength. Geopolymer with the maximum compressive strength was synthesized of the most reactive FA in the reaction of alkali activation i.e. which had the highest content of particles smaller than 43 m, glassy phase, and soluble silicon and aluminum in a strongly alkaline medium. On the other hand, geopolymer with minimum compressive strength was synthesized of less reactive FA, which had lower content of particles smaller than 43 m, glassy phase, and soluble silicon and aluminum. Geopolymers based on selected FA samples represented the reference system in further research and were synthesized at room temperature (20 °C) with the reaction time of 28 days..

On the existence for diffeo-integral inclusion of Sobolev-type of fractional order with applications

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