in this work, we have applied elzaki transform and he's homotopy perturbation method to solvepartial dierential equation (pdes) with time-fractional derivative. with help he's homotopy per-turbation, we can handle the nonlinear terms. further, we have applied this suggested he's homotopyperturbation method in order to reformulate initial value problem. some illustrative examples...

In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM was utilized establish approximate series solutions. technique considered be an extension original Adams–Bashforth–Moulton approach. Numerical simulations and figures are discussed, in order show efficiency of proposed method. futur...

*Correspondence: [email protected] 1School of Mathematics and Physics, China University of Geosciences, Lumo 388, Wuhan, 430074, China Full list of author information is available at the end of the article Abstract In this paper we start by giving a new definition of weak Caputo derivative in the sense of distributions, and we give a variational formulation to a fractional diffusion equa...

and Applied Analysis 3 fractional order to distributed order fractional. In Section 4, we introduce the distributed order fractional evolution systems C doD α t x t A C doD β t x t Bu t , x 0 x0, 0 < β < α ≤ 1, 1.5 where u t is control vector, and generalize the results obtained in Section 3 for this case. Finally, the conclusions are given in the last section. 2. Elementary Definitions and The...

ABSTRACT. In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order α are studied. We present four types of Ulam stability results for the fractional differential equation in the case of 0 < α < 1 and b = +∞ by virtue of the Henry-Gronwall inequality. Meanwhile, we give an interesting data dependence results for the fracti...

We study the existence and uniqueness of solutions for coupled Langevin differential equations fractional order with multipoint boundary conditions involving generalized Liouville–Caputo derivatives. Furthermore, we discuss Ulam–Hyers stability in context problem at hand. The results are shown examples. Results asymmetric when a derivative (ρ) parameter is changed.

In this paper, we consider a class of abstract Cauchy problems in the framework generalized Caputo type fractional. We discuss existence and uniqueness mild solutions to such fractional differential equations by using properties found related calculus, theory uniformly continuous semigroups operators fixed point theorem. Moreover, dependence on parameters Ulam stability solutions. At end bring ...

The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal contro...

In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with spaceand time-fractional derivatives. The new generalization is based on the two-dimensional differential transform method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrat...