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Positive solutions of fractional integral equations by the technique of measure of noncompactness

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

A short note on C ∗ -valued contraction mappings

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.

On the existence of solution for fractional differential equations of order 3 < δ 1 ≤ 4

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...

The existence of solutions for some fractional finite difference equations via sum boundary conditions

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...

Existence and uniqueness of positive solutions to fractional boundary value problems with nonlinear boundary conditions

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.

Some existence results for a nonlinear fractional differential equation on partially ordered Banach spaces

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.

Best proximity and fixed point results for cyclic multivalued mappings under a generalized contractive condition

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

Nonlinear -Fuzzy stability of cubic functional equations

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