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  • Collection: Review Articles

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers arepresented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.

The fractional-order derivative of a non-constant periodic function is not periodic with the same period. Consequently, any time-invariant fractional-order systems do not have a non-constant periodic solution. This property limits the applicability…

In this paper, we study the existence of a continuous solution for a nonlinear integral equation of a product type. The analysis uses the techniques of measures of noncompactness and Darbo's fixed point theorem. Our results are obtained under rather…

In this paper, we first introduce the conformable fractional Laplace transform. Then, we give its generalization for higher-order. Finally, as an application, we solve a non-homogeneous conformable fractional differential equation with variable…

In this work, we study the existence and the asymptotic stability of the continuous solutions for a general form for neutral integral equations of product type. Our result will given in more general and easy conditions; Moreover, the neutral integral…

 In this paper, we construct the solution expressions of fourth order nonlinear difference systems

Φn+1       =                   Φn−2Ψn−3                       ,
        α + Ψn (±1 ± Γn−1Φn−2Ψn−3)
Ψn+1       =                  …

 In this work, we propose a new directed digital signature scheme over a group ring whose security relies on the hardness of the discrete logarithm problem and the factorization search problem. This scheme is efficient as it requires very few…

In this paper, we prove the existence and regularity of solutions for a class of nonlinear anisotropic degenerate elliptic equations with the data f belonging to certain Marcinkiewicz spaces Mm(Ω) with m > 1. We use a generalized Stampacchia Lemma…

This paper aims to explore the existence results of a certain type of Caputo fractional qq-difference equations in Banach spaces. To achieve this goal, we employ a fixed point theorem that relies on the concept of measure of noncompactness and the…

In this paper, we will study the maximum number of limit cycles of a perturbed differential system with respect to its parameters which appear in the system specially on the degree of the polynomials. For this we will use two methods namely the…
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