In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of Volterra-Fredholm type differential equations with nonlocal conditions in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques.
Strictly Chordality-k graphs (SC k graphs) are graphs which are either cycle free or every induced cycle is exactly k, for some fixed k, k ≥ 3. Note that k = 3 and k = 4 are precisely the Chordal graphs and Chordal Bipartite graphs, respectively. In this paper, we initiate a structural and an algo-rithmic study of SC k , k ≥ 5 graphs.
For a connected graph, a minimum vertex separator is a minimum set of vertices whose removal creates at least two connected components. The vertex connectivity of the graph refers to the size of the minimum vertex separator and a graph is k-vertex connected if its vertex connectivity is k, k ≥ 1. Given a k-vertex connected graph G, the combinatorial problem… (More)
In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of Volterra-Fredholm type differential equations with impulses in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. ifx
Deregulation is, restructuring the rules and economic incentives that the government setup to control and drive the Electric Supply Industry (ESI). It is also called as open power market, competitive power market, vertically unbundled market etc. With the introduction of deregulation, the electric power industry needs changes in various power system… (More)
Strictly Chordality-k graphs (SC k) are graphs which are either cycle-free or every induced cycle is of length exactly k, k ≥ 3. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal bipartite graphs, respectively. For k ≥ 5, the study has been recently initiated in  and various structural and algorithmic results are… (More)
A vertex separator of a connected graph G is a set of vertices removing which will result in two or more connected components and a minimum vertex separator is a set which contains the minimum number of such vertices, i.e., the cardinality of this set is least among all possible vertex separator sets. The cardinality of the minimum vertex separator refers… (More)
India is world's largest democracy. Fundamental right to vote or simply voting in elections forms the basis of Indian democracy. In India all earlier elections a voter used to cast his vote by using ballot paper. This is a long, time-consuming process and very much prone to errors. This situation continued till election scene was completely changed by… (More)