We consider a fractional differential equation of order α, α∈(2,3], involving ψ-Caputo derivative subject to initial conditions on function and its first an integral boundary condition that depends the unknown function. As application, we investigate world population growth. find α ψ for which solution our model describes given real data better than available models.

We establish some common best proximity point results for generalized α−ψ-proximal contractive non-self mappings. We provide some concrete examples. We also derive some consequences on some best proximity results on a metric space endowed with a graph. 2000 Mathematics Subject Classification: 47H10, 54H25.

where φ, ψ ∈ L, H = −~ 2m ∆+V (~x) is essentially self-adjoint, H̄ is the closure ofH , and φ, ψ, V each carries at most a finite number of singularities and discontinuities. In flavor of physics literature, we will formulate the Feynman path integral with improper Riemann integrals. In hope that with further research we can formulate a rigorous polygonal path integral, we will also provide a No...

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of browder-petryshyn type mapping. our resultsimprove and extend the results announced by many others.

where dA is the normalized area measure in D. The case where α = 0 is known as the (unweighted) Bergman space, often simply denoted by A2. Let φ be an analytic map from the open unit disk D into itself. The operator that takes the analytic map f to f ◦ φ is a composition operator and is denoted by Cφ . A natural generalization of a composition operator is an operator that takes f to ψ · f ◦ φ, ...

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric ...