n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

In this paper, we studied the existence results for solutions of a new class fractional boundary value problem in Caputo–Hadamard settings. Moreover, conditions were formulated as mixed multi-order Hadamard integro-derivative conditions. To prove main results, applied two well-known techniques topological degree and fixed point theories. Finally, provide examples to show compatibility our theor...

This paper presents a novel-fractional-order lithium-ion battery model that is suitable for use in embedded applications. The proposed model uses fractional calculus with an improved Oustaloup approximation method to describe all the internal battery dynamic behaviors. The fractional-order model parameters, such as equivalent circuit component coefficients and fractional-order values, are ident...

This paper investigates the existence of solutions for higher order fractional differential inclusions with fractional integral boundary conditions involving nonintersecting finite many strips of arbitrary length. Our study includes the cases when the right-hand side of the inclusion has convex as well non-convex values. Some standard fixed point theorems for multivalued maps are applied to est...

‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and ...

the paper is devoted to the study of brenstien polynomials and development of some new operational matrices of fractional order integrations and derivatives. the operational matrices are used to convert fractional order differential equations to systems of algebraic equations. a simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

The paper discusses several control techniques for a class of systems described by fractional order equations. presents the unit frequency criteria that ensure closed loop for: Fractional Order Linear Systems, Systems with nonlinear components, Time Delay components. stability criterion is proposed composed subsystems. These are used in two applications: Soft Exoskeleton Glove Control, studied ...

Necessary and sufficient stability instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives constant coefficients. In both cases, fractional-order-dependent as well fractional-order-independent characterisations of properties obtained, in terms the coefficients equation. The theoretical results exemplified particular c...