In this paper, we study the existence of solutions for nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with three-point boundary conditions by using measure noncompactness combined fixed point theorem M?nch. An example illustrating effectiveness theoretical results is presented.

We prove new inequalities for the spectral radius, essential operator norm, measure of noncompactness and numerical radius Hadamard weighted geometric means positive kernel operators on Banach function sequence spaces. Some extend refine known that have been established by several authors relatively recently. Several appear to be even in finite dimensional case.

In this paper, we consider the newly defined partial (?,?)-fractional integral and derivative to study a new class of fractional differential equations with impulses. The existence Ulam-Hyers stability solutions for proposed equation are investigated via means measure noncompactness fixed point theorems. presented results quite general in their nature further complement existing ones.

The original approach of Hutchinson to fractals considers the defining equation as a fixed point problem, and then applies Banach Contraction Principle. To do this, Blaschke Completeness Theorem is essential. Avoiding Blaschke’s result, this note presents an alternative way via Kuratowski noncompactness measure. Moreover, our technique extends existence part Hutchinson’s condensing maps instead...