[PDF] Top 20 A conformable fractional calculus on arbitrary time scales
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A conformable fractional calculus on arbitrary time scales
... Fractional calculus is nowadays one of the most intensively devel- oping areas of mathematical analysis ( Jahanshahi et ...of fractional operators like Riemann–Liouville, Caputo, and ...for ... See full document
6
Existence and uniqueness results for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary time scales
... the time-scale community or by the fractional one. Results on fractional dynamic equations on time scales are scarce ( Ahmadkhanlu and Jahanshahi, 2012 ... See full document
5
Existence and uniqueness of solution for a fractional Riemann-Liouville initial value problem on time scales
... functions on a general complete metric space. Roughly speaking, the calculus on time scales begins by introducing and investigating the concept of deriva- tive for functions f : T ! ... See full document
6
Existence of solution to a nonlocal conformable fractional thermistor problem
... strongly on the ...with fractional-order derivatives were ...a fractional Caputo nonlocal thermistor problem ...a fractional Riemann–Liouville nonlocal thermistor problem on ... See full document
12
Necessary condition for an Euler-Lagrange equation on time scales
... delta calculus on time scales, which will be used throughout the ...the calculus of variations on an arbitrary time scale (Theorem ...equation on time ... See full document
8
Calculus of variations on time scales and applications to economics
... paid on two inverse extremal problems on arbitrary time ...quantum calculus are obtained as particular ...problems, on an arbitrary time scale, are ...of ... See full document
138
A table of derivatives on arbitrary time scales
... classical calculus, integration on time scales is the inverse operation of differentiation, that is, the delta integral is defined as the antiderivative with respect to the delta ... See full document
7
Linear fractional discrete-time systems
... of time scales will not be used in its full ...(2003). Time scales theory aims at unifying continuous and discrete analysis by defining calculus on any closed set T ⊆ R, called ... See full document
6
Discrete Direct Methods in the Fractional Calculus of Variations
... of fractional derivatives. The arbitrary order derivative of a function at a time t depends on all values of that function in ( −∞, t] and [t, ∞) because of the infinite sum, backward and ... See full document
6
Calculus of variations on time scales and discrete fractional calculus
... The calculus of variations deals with finding extrema and, in this sense, it can be considered a branch of ...domain on the quantity to be optimized. The calculus of variations is concerned with ... See full document
116
On the initial conditions in continuous-time fractional linear systems
... term on the right in (4) is constituted by the deriva- tives of the Heaviside functions that we are needing for making continuous the left hand function before computing the ... See full document
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ON LIAPUNOV-TYPE INTEGRAL INEQUALITIES FOR EVEN ORDER DYNAMIC EQUATIONS ON TIME SCALES
... Then f is increasing, decreasing, nonincreasing, and nondecreasing on [a, b] if f ∆ (t) > 0, f ∆ (t) < 0, f ∆ (t) ≤ 0, f ∆ (t) ≥ 0, for all t ∈ [a, b), respectively. We will make use of the following product ... See full document
12
Isoperimetric problems of the calculus of variations with fractional derivatives
... A fractional derivative is a generalization of the ordinary differentiation, which allows real number powers of the differential ...of fractional derivatives to several fields, like geometry, physics, ... See full document
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Necessary optimality conditions for infinite horizon variational problems on time scales
... equations on a time scale or a measure chain [ 1 , 2 , 8 ...above time scale differential equations must also come from minimization of some delta or nabla functional with a Lagrangian containing ... See full document
16
On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales
... Let T be a time scale, i.e., a nonempty closed subset of R. For a, b ∈ T, we define the closed interval [a , b] T by [a, b] T = {t ∈ T : a 6 t 6 b}. The open and half-open intervals are defined in a similar way. ... See full document
14
Multidimensional time fractional diffusion equation
... about fractional calculus and special ...the time fractional diffusion ...the fractional moments of arbitrary order γ > 0 and in Section 5 we present some plots of the ... See full document
8
On consensus in the Cucker--Smale type model on isolated time scales
... Abstract. This article addresses a consensus phenomenon in a Cucker-Smale model where the magnitude of the step size is not necessarily a constant but it is a function of time. In the considered model the weights ... See full document
14
Exercises on Integral Calculus
... One lets a ball to fall down from a height h; every time the ball reaches the oor it jumps until 2/3 of the previous height.. What is the total distance (up and down) covered by the bal[r] ... See full document
12
Computational methods in the fractional calculus of variations and optimal control
... depending on a Caputo fractional derivative, a fractional and an indefi- nite ...give fractional Euler–Lagrange type equations and natural boundary conditions, which provide a generalization ... See full document
193
Oscillation Theorems of Fourth Order Nonlinear Dynamic Equations on Time Scales
... of time scales which has recently received a lot of attention was introduced by Stefan Hilger in his ...expounded on various aspects of this new theory and for more details about the theory of ... See full document
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