Solving a well-posed fractional initial value problem by a complex approach

Well-Posed Initial-Boundary Value Problem for Constrained Evolution

A 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...

Positive solutions for discrete fractional initial value problem

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...

Modified fractional Euler method for solving Fuzzy sequential Fractional Initial Value Problem under H-differentiability

In this paper, the solution to Fuzzy sequential Fractional Initial Value Problem [FFIVP] under Caputo type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylors formu...

Generalized Tableaux and Formally Well-posed Initial Value Problems

We generalize the notion of a tableau of a system of partial diierential equations. This leads to an intrinsic deenition of formally well-posed initial value problems, i.e. problems with exactly the right amount of Cauchy data. We must allow here that the data is prescribed on a ag of submanifolds. The advantage of this approach is that even for non-normal systems the data can be chosen complet...