Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives

Initial time difference quasilinearization for Caputo Fractional Differential Equations

Correspondence: [email protected]. tr Department of Statistics, Gaziosmanpasa University, Tasliciftlik Campus, 60250 Tokat, Turkey Abstract This paper deals with an application of the method of quasilinearization by not demanding the Hölder continuity assumption of functions involved and by choosing upper and lower solutions with initial time difference for nonlinear Caputo fractional different...

Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales

‎In this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1

Numerical Methods for Sequential Fractional Differential Equations for Caputo Operator

To obtain the solution of nonlinear sequential fractional differential equations for Caputo operator two methods namely the Adomian decomposition method and DaftardarGejji and Jafari iterative method are applied in this paper. Finally some examples are presented to illustrate the efficiency of these methods. 2010 Mathematics Subject Classification: 65L05, 26A33

Fractional Derivatives, Fractional Integrals, and Fractional Differential Equations in Matlab

The term fractional calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to non-integer (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. In a letter to L’Hospital in 1695 Leibniz raised the following question (Miller and Ross...

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications