A note on the initial value problem of fractional evolution equations
نویسندگان
چکیده
منابع مشابه
On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales
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.
متن کاملA distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations
The fractional calculus deals with the generalization of integration and differentiation of integer order to those ones of any order. The q-fractional differential equation usually describe the physical process imposed on the time scale set Tq. In this paper, we first propose a difference formula for discretizing the fractional q-derivative of Caputo type with order and scale index . We es...
متن کاملOn boundary value problem for fractional differential equations
In this paper, we study the existence of solutions for a fractional boundary value problem. By using critical point theory and variational methods, we give some new criteria to guarantee that the problems have at least one solution and infinitely many solutions.
متن کاملPositive Solutions for the Initial Value Problem of Fractional Evolution Equations
and Applied Analysis 3 Clearly, if the semigroup S(t) (t ≥ 0) is positive, then, by the definitions, the operators U(t) and V(t) are also positive for all t ≥ 0. The following lemma follows from the results in [14, Lemma 2.9] and [15, Lemmas 3.2–3.5]. Lemma 6. The operators U(t) and V(t) have the following properties. (i) For any fixed t ≥ 0 and any x ∈ Xα, one has ‖U(t)x‖α ≤ M‖x‖α, ‖V(t)x‖α ≤ ...
متن کاملon the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2015
ISSN: 1687-1847
DOI: 10.1186/s13662-015-0470-2