Browsing by Author "Salehi, Saeid"

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A k-Dimensional System of Fractional Finite Difference Equations
(2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.
Citation - WoS: 38
Citation - Scopus: 42
The Existence of Solutions for Some Fractional Finite Difference Equations Via Sum Boundary Conditions
(Springer, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; Agarwal, Ravi P.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript we investigate the existence of the fractional finite difference equation (FFDE) Delta(mu)(mu-2)x(t) = g(t + mu - 1, x(t + mu - 1), Delta x(t + mu - 1)) via the boundary condition x(mu - 2) = 0 and the sum boundary condition x(mu + b + 1) = Sigma(alpha)(k=mu-1) x(k) for order 1 < mu <= 2, where g : N-mu-1(mu+b+1) x R x R -> R, alpha is an element of N-mu-1(mu+b), and t is an element of N-0(b+2). Along the same lines, we discuss the existence of the solutions for the following FFDE: Delta(mu)(mu-3)x(t) = g(t + mu - 2, x(t + mu - 2)) via the boundary conditions x(mu - 3) = 0 and x(mu + b + 1) = 0 and the sum boundary condition x(alpha) = Sigma(beta)(k=gamma)x(k) for order 2 < mu <= 3, where g : N-mu-2(mu+b+1) x R -> R, b is an element of N-0, t is an element of N-0(b+3), and alpha, beta,gamma N-mu-2(mu+b) with gamma < beta < alpha.
Citation - WoS: 5
A Fractional Finite Difference Inclusion
(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript we investigated the fractional finite difference inclusion Delta(mu)(mu-2) x(t) is an element of F(t, x(t), Delta x(t)) via the boundary conditions Delta x(b + mu) = A and x(mu - 2) = B, where 1 <= 2, A,B is an element of R and F :N-mu-2(b+mu+2) x R -> 2(R) is a compact valued multifunction.
Citation - WoS: 6
Citation - Scopus: 13
A K-Dimensional System of Fractional Finite Difference Equations
(Hindawi Ltd, 2014) Rezapour, Shahram; Salehi, Saeid; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.
Citation - WoS: 5
Citation - Scopus: 7
On Some Self-Adjoint Fractional Finite Difference Equations
(Eudoxus Press, Llc, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently, the existence of solution for the fractional self-adjoint equation Delta(nu)(nu-1) (p Delta y)(t) = h(t) for order 0 < nu <= 1 was reported in [9]. In this paper, we investigated the self-adjoint fractional finite difference equation Delta(nu)(nu-2)(p Delta u(t) = j(t,p(t+nu - 2)) via the boundary conditions y(nu - 2) = 0 , such that Delta y(nu - 2) = 0 and Delta y(nu+b) = 0. Also, we analyzed the self-adjoing fractional finite difference equation Delta(nu()(nu-2)p Delta(2)y)(t) = j(t,[(t+nu - 2)Delta(2)y(t+nu-3)) via the boundary conditions y(nu - 2) = 0, Delta y(nu - 2) = 0, Delta(2)y(nu - 2) = 0 and Delta 2y(nu+b) = 0. Finally, we conclude a result about the existence of solution for the general equation Delta(nu()(nu-2)p Delta(m)y)(t) = h(t,p(t+nu - m - 1)Delta(m)y(t+nu - m - 1)) via the boundary conditions y(nu - 2) = Delta y(nu - 2) = Delta(2)y(nu - 2) = center dot center dot center dot Delta(m)y(nu+b) = 0 for oder 1 < nu <= 2.
Citation - WoS: 7
Citation - Scopus: 12
On the Existence of Solutions for a Fractional Finite Difference Inclusion Via Three Points Boundary Conditions
(Springer, 2015) Rezapour, Shahram; Salehi, Saeid; Baleanu, Dumitru; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we discussed the existence of solutions for the fractional finite difference inclusion Delta(nu)x(t) is an element of F(t, x(t), Delta x(t), Delta(2)x(t)) via the boundary value conditions xi x(nu - 3) + beta Delta x(nu - 3) = 0, x(eta) = 0, and gamma x(b + nu) + delta Delta x(b + nu) = 0, where eta is an element of N-nu-2(b+nu-1), 2 < nu < 3, and F : N-nu-3(b+nu+1) x R x R x R -> 2(R) is a compact valued multifunction.