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 Communications in Advanced Mathematical SciencesNumber of Followers: 0     Open Access journal ISSN (Print) 2651-4001 Published by DergiPark  [187 journals]
• A Nonlinear $r(x)$-Kirchhoff Type Hyperbolic Equation: Stability Result
and Blow up of Solutions with Positive Initial Energy

• Authors: Mohammad SHAHROUZİ; Jorge FERREIRA
Abstract: In this paper we consider $r(x)-$Kirchhoff type equation with variable-exponent nonlinearity of the form $$u_{tt}-\Delta u-\big(a+b\int_{\Omega}\frac{1}{r(x)} \nabla u ^{r(x)}dx\big)\Delta_{r(x)}u+\beta u_{t}= u ^{p(x)-2}u,$$ associated with initial and Dirichlet boundary conditions. Under appropriate conditions on $r(.)$ and $p(.)$, stability result along the solution energy is proved. It is also shown that regarding arbitrary positive initial energy and suitable range of variable exponents, solutions blow-up in a finite time.
PubDate: Mon, 27 Dec 2021 00:00:00 +030

• Results on the Behavior of the Solutions for Linear Impulsive Neutral
Delay Differential Equations with Constant Coefficients

• Authors: Ali Fuat YENİÇERİOĞLU
Abstract: We have given some results regarding the behavior of solutions for first order linear impulsive neutral delaydifferential equations with constant coefficients. These results were obtained using two different real roots of thecorresponding characteristic equation. Finally, two examples are given for solutions of impulsive neutral delaydifferential equations.
PubDate: Mon, 27 Dec 2021 00:00:00 +030

• On Recursive Hyperbolic Fibonacci Quaternions

• Authors: Ahmet DAŞDEMİR
Abstract: Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers. This article presents new classes of quaternions whose components are composed of symmetrical hyperbolic Fibonacci functions. In addition, the Binet's formulas, certain generating matrices, generating functions, Cassini's and d'Ocagne's identities for these quaternions are given.
PubDate: Mon, 27 Dec 2021 00:00:00 +030

• Padovan and Perrin Hybrid Number Identities

• Authors: Renata VİEİRA; Milena MANGUEİRA, Francisco Regis ALVES, Paula Maria Machado CRUZ CATARİNO
Abstract: This work investigates the numbers of Padovan and Perrin hybrids. At first, the hybrid numbers, the sequences in the hybrid form, and their matrix forms are ordered as studied sequences. Thus, it was possible to display the negative index hybrids, define some identities belonging to these hybrid sequences, develop novel theorems and present them as binomial sums of the Padovan and Perrin hybrids.
PubDate: Mon, 27 Dec 2021 00:00:00 +030

• On the Solutions of the Higher Order Fractional Differential Equations of
Riesz Space Derivative with Anti-Periodic Boundary Conditions

• Authors: Şuayip TOPRAKSEVEN
Abstract: We present existence and uniqueness results for a class of higher order anti-periodic fractional boundary value problems with Riesz space derivative which is two-sided fractional operator. The obtained results are established by applying some fixed point theorems. Various numerical examples are given to illustrate the obtained results.
PubDate: Mon, 27 Dec 2021 00:00:00 +030

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