In this paper, we define the fuzzy Henstock-Δ-integral and Δ-derivative on time scales(or briefly FH-Δ-integral, Δ-derivative). Then, give some convergence theorems for kind of nonabsolute convergent integrals. Finally, obtain an existence theorem global solutions generalized differential systems.

Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...

a f(x, y) dy, it is often important to know when F is differentiable and when F (x) = ∫ b a f1(x, y) dy. A sufficient condition for differentiating under the integral sign is that ∫ b a f1(x, y) dy converges uniformly; see [6, p. 260]. When we have absolute convergence, the condition |f1(x, y)| ≤ g(y) with ∫ b a g(y) dy < ∞ suffices (Weierstrass M-test and Lebesgue Dominated Convergence). If we...

If f is a Henstock-Kurzweil integrable function on the real line, the Alexiewicz norm of f is ‖f‖ = sup I | ∫ I f | where the supremum is taken over all intervals I ⊂ . Define the translation τx by τxf(y) = f(y − x). Then ‖τxf − f‖ tends to 0 as x tends to 0, i.e., f is continuous in the Alexiewicz norm. For particular functions, ‖τxf − f‖ can tend to 0 arbitrarily slowly. In general, ‖τxf − f‖...

The dual space of the class of Henstock-Kurzweil integrable functions is well known in the one-dimensional case and corresponds to the space of multipliers which, in turn, coincides with the class of functions of bounded essential variation. Comparable results in higher dimensions have been elusive. For cases in which the partitions defining the Henstock-Kurzweil integrals are defined on n-cell...

By using the properties of strong fuzzy Henstock integrals, the existence theorems of solution for a kind of the discontinuous fuzzy Fredholm integral equations are established. The results are generalizations of earlier investigation for fuzzy continuous systems.

Some recent results related to the P-adic derivatives and integrals are surveyed. Applications of the Henstock-Kurzweil P-integral and the Perron P-integral to the problem of recovering the coefficients of series with respect to the Vilenkin system and the Haar system (both in one dimension and in higher dimensions) are discussed. The case of the continual analogue of the Vilenkin system is als...

in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...