Fractional calculus in viscoelasticity: An experimental study

On the existence of solutions of fractional integro-differential equations

“…The book by Klafter et al [19] covers the latest developments in the field of fractional dynamics. Besides the mentioned books, there are several papers about the applications of the fractional calculus in signal processing, complex dynamics in biological tissues, viscoelastic materials, thermal systems and heat conduction (for example, see [25]- [27], [34] and [37]). In recent years, many works on fractional differential and integral equations are dealing with the existence and uniqueness of solutions.…”

Helical flows of fractionalized Burgers' fluids

“…Some other interesting results and discussion of fractional calculus approach in viscoelasticity can be found in. [29][30][31] The aim of this communication is to find some new and simple results for the helical flows of rate type fluids. More exactly, our interest is to find the velocity field and the shear stress corresponding to the motion of a Burgers' fluid in a cylinder that at the initial moment begins to rotate around its axis with an angular velocity t, and to slide along the same axis with linear velocity Ut.…”

Discrete-Time Fractional Optimal Control

“…This is fixed final state problem, so x(10) is known. Using this value we can obtain λ (10). Once λ(10) is known, we can obtain state variable vector x(k).…”

“…Once λ(10) is known, we can obtain state variable vector x(k). Substituting x(k) and λ (10) in Equation (36) we get the co-state vector λ(k). Using λ(k) in Equation (31) we get the control vector u(k).…”