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**Agarwal** 2
Manuel De la Sen 0
0 Institute of Research and Development of Processes IIDP Faculty of Science and Technology, University of the Basque Country , Leioa , Spain
1 Department of Mathematics, Sari

In this short note we point out that the recently announced notion, the C ∗ -valued metric, does not bring about a real extension in metric fixed point theory. Besides, fixed point results in the C ∗ -valued metric can be derived from the desired Banach mapping principle and its famous consecutive theorems.

In this paper, we deal with a fractional differential equation of order δ 1 ∈ ( 3 , 4 ] with initial and boundary conditions, D δ 1 ψ ( x ) = − H ( x , ψ ( x ) ) , D α 1 ψ ( 1 ) = 0 = I 3 − δ 1 ψ ( 0 ) = I 4 − δ 1 ψ ( 0 ) , ψ ( 1 ) = Γ ( δ 1 − α 1 ) Γ ( ν 1 ) I δ 1 − α 1 H ( x , ψ ( x ) ) ( 1 ) , where x ∈ [ 0 , 1 ] , α 1 ∈ ( 1 , 2 ] , addressing the existence of a positive...

In this manuscript we investigate the existence of the fractional finite difference equation (FFDE) Δμ−2μx(t)=g(t+μ−1,x(t+μ−1),Δx(t+μ−1)) via the boundary condition x(μ−2)=0 and the sum boundary condition x(μ+b+1)=∑k=μ−1αx(k) for order 1<μ≤2, where g:Nμ−1μ+b+1×R×R→R, α∈Nμ−1μ+b, and t∈N0b+2. Along the same lines, we discuss the existence of the solutions for the following FFDE...

In this manuscript, we consider two problems of boundary value problems for a fractional differential equation. A fixed point theorem in partially ordered sets and a contraction mapping principle are applied to prove the existence of at least one positive solution for both fractional boundary value problems.MSC: 47H10, 26A33, 34A08.

By using fixed point results on cones, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Examples are presented in order to illustrate the obtained results.

Eshaghi Gordji
Asier Ibeas
**Ravi** **P** **Agarwal**
0 Institute of Research and Development of Processes, University of Basque Country, Campus of Leioa (Bizkaia) - Aptdo. 644 - Bilbao , Bilbao, 48080 , Spain
This

Journal of Inequalities and Applications
Nonlinear L-Fuzzy stability of cubic functional equations
**Ravi** **P** **Agarwal** agarwal@tamuk 0
Yeol Je Cho
Reza Saadati
Shenghua Wang
0 Department of Mathematics