Research ArticleOpen accessEvery word in the titleSome Contributions to the Theory of Abstract Degenerate Volterra Integro-Differential EquationsMarko KostićIn this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equations with Caputo derivatives by using the pure Laplace transform techniques. …Journal of Mathematics and Statistics, Vol. 12, Issue 2 · 17 Jun 2016 · 7,406 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleLOCAL FRACTIONAL VARIATIONAL ITERATION METHOD FOR SOLVING VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITHIN LOCAL FRACTIONAL OPERATORSAmmar Ali NeamahThe paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations. …Journal of Mathematics and Statistics, Vol. 10, Issue 3 · 9 Oct 2014 · 6,511 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn the Theory of Intuitionistic Fuzzy N-Inner Product Spaces with ApplicationsRenu Chugh, Seema MehraProblem statement: The purpose of this study was to introduce the notion of Intuitionistic fuzzy n-inner product space and to prove a fixed point theorem in complete intuitionistic fuzzy ninner product space. Conclusion/Recommendations: Further this result is applied to obtain the existence and uniqueness of solution for linear volterra integral equation. …Journal of Mathematics and Statistics, Vol. 8, Issue 2 · 19 Mar 2012 · 7,727 accessesView PDFCite
Research ArticleOpen accessIn the keywordsSolving Volterra's Population Model Using New Second Derivative Multistep MethodsK. Parand, G. HojjatiIn this study new second derivative multistep methods (denoted SDMM) are used to solve Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential where the integral term represents the effect of toxin. This model is first converted to a nonlinear ordinary differential equation and then the new SDMM, which has good … …American Journal of Applied Sciences, Vol. 5, Issue 8 · 31 Aug 2008 · 6,908 accessesView PDFCite
Research ArticleOpen accessIn the keywordsFlow of Dividends under a Constant Force of InterestJuma Kasozi, Jostein PaulsenThis study addresses the issue of maximization of dividends of an insurer whose portfolio is exposed to insurance risk. The insurance risk arises from the classical surplus process commonly known as the Cramér-Lundberg model in the insurance literature. To enhance his financial base, the insurer invests in a risk free asset whose price dynamics are governed by a constant force … …American Journal of Applied Sciences, Vol. 2, Issue 10 · 31 Oct 2005 · 7,386 accessesView PDFCite
Research ArticleOpen accessIn the keywordsNumerical Ultimate Ruin Probabilities under Interest ForceJuma Kasozi, Jostein PaulsenThis work addresses the issue of ruin of an insurer whose portfolio is exposed to insurance risk arising from the classical surplus process. Availability of a positive interest rate in the financial world forces the insurer to invest into a risk free asset. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block … …Journal of Mathematics and Statistics, Vol. 1, Issue 3 · 30 Sep 2005 · 6,491 accessesView PDFCite