Caputo fractional derivativeCaputo–Hadamard fractional derivativefundamental theorem of fractional calculus26A33In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. ...
Fractional differential equations with dependence on the Caputo-Katugampola derivative In this paper, we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives...
for Caputo fractional mixed Volterra–Fredholm-type integro-differential inclusions of orderwith sectorial operators. Controllability is the capability of a control system to be directed from an arbitrary initial state to a likewise arbitrary final state through the permitted set of controls, for example...
Analysis: Caputo type q-fractional derivative The Caputo type q-fractional initial value problem with 0 < q < 1 and 0 < α < 1 can be stated as follows:cDqαx(t)=f(t,x(t)),t0<t≤a,x(t0)=x0,0<α<1, where t0 ∈ Tq, the time scale Tq={qn:n∈Z}...
This work considers a generalized fuzzy fractional smoking model with Caputo gHtypes fractional derivatives upon considering the case of uncertainty quantification. The disease-free equilibrium point and stability of the equilibrium point have been discussed for the fuzzy nonlinear fractional smoking model....
A Lavrent'ev-type approach to the on-line computation of Caputo fractional derivatives* The computation of Caputo fractional derivatives is an ill-posed problem (in fact a special deconvolution problem) which can be approached using suitable r... L Pandolfi - 《Inverse Problems》 被引量: 7...
4, For every, The fractal fractional derivative of Caputo Fabrizio type concerning exponential decay kernel is defined by, $${D}_{t}^{a,b}\left(C\left(t\right)\right)=\frac{M\left(a\right)}{1-a}\int\limits_{\alpha}^{{t}}\frac{dC\left(s\right)}{d{s}^{b}}{\exp}\left[...
Alzahrani, F.S., Abbas, I.A.: Fractional order GL model on thermoelastic interaction in porous media due to pulse heat flux. Geomech. Eng. 23, 217–225 (2020) MATH Google Scholar Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract...
A new generalised Caputo fractional operator is introduced.The generalised operator is shown to have higher degree of freedom (DF).Some basic mathematical properties of the new fractional operator are discussed.The new operator is applied to two predator-prey systems; the HP and GLV systems.Various...
Riemann–Liouville fractional derivative: Which was presented by Riemann in 1847, and take the form: Dtαf(t)=1Γ(n−α)dndtn∫atf(x)(t−x)α−n+1dx,0<α<n 3. Caputo derivative: Caputo derivative45was acquired in 1967. It was defined as: ...