Fractional Boundary Value Problems with Multiple Orders of Fractional Derivatives and Integrals
نویسندگان
چکیده
In this article we study a new class of boundary value problems for fractional differential equations and inclusions with multiple orders of fractional derivatives and integrals, in both fractional differential equation and boundary conditions. The Sadovski’s fixed point theorem is applied in the single-valued case while, in multi-valued case, the nonlinear alternative for contractive maps is used. Some illustrative examples are also included.
منابع مشابه
The Study of Some Boundary Value Problems Including Fractional Partial Differential Equations with non-Local Boundary Conditions
In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations (FPDE) with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...
متن کاملHigher order multi-point fractional boundary value problems with integral boundary conditions
In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...
متن کاملNumerical solution for boundary value problem of fractional order with approximate Integral and derivative
Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...
متن کاملExistence of three solutions for a class of fractional boundary value systems
In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of t...
متن کاملB-Spline Solution of Boundary Value Problems of Fractional Order Based on Optimal Control Strategy
In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...
متن کامل