Fractional calculus has been proved to be very effective in representing the visco-elastic relaxation response of materials with memory such as polymers. Moreover, modeling temperature dependency material functions thermo-visco-elasticity, standard time–temperature superposition principle is known ineffective most cases (thermo-rheological complexity). In this work, a novel finite element formu...

Article history: Received 1 June 2014 Received in revised form 15 April 2015 Accepted 29 April 2015 Available online 5 May 2015

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

In this paper, we study optimal control problems for nonlinear fractional order boundary value on a star graph, where the derivative is described in Caputo sense. The adjoint state and optimality system are derived problem (FOCP) by using Lagrange multiplier method. Then, existence uniqueness of solution equation proved means Banach contraction principle. We also pr...

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

Bilgisayar teknolojilerindeki gelişmeler zor ve karmaşık hesaplamalar içeren kesirli matematik alanına olan ilgiyi arttırmıştır. Özellikle, gerçek sistemleri modellemedeki başarısı nedeniyle kontrol alanında çokça yararlanılmaktadır. Pek çok çalışma yapılmasına rağmen matematiği literatürde hala çözümsüz durumlar bulunmaktadır. Kontrol kullanımında karşılaşılan en büyük zorluk analitik çözüm ek...

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...