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  • Collection: Review Articles

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…

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, 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.

In this work, we show that the system of difference equationsxn+1=(ayn-2xn-1yn+bxn-1yn-2+cyn-2+d)/(yn-2xn-1yn),yn+1=(axn-2yn-1xn+byn-1xn-2+cxn-2+d)/(xn-2yn-1xn),where n belongs to the set of positive integer numbers, x-2, x-1, x0, y-2, y-1 and y0 are…

The aim of this work is to study the existence of solutions to a class of fractional differential equations with a mixed of fractional integral boundary conditions involving the Hilfer fractional derivative. The proof is based on Monch's fixed point…

In this paper, the Taylor collocation method is applied to numerically solve a kth-order neutral linear Volterra integro-differential equation with constant delay and variable coefficients.We also provide a rigorous analysis to estimate the…

 Recently, we have introduced the notion of standard single valued neutrosophic (SSVN) metric space as a generalization of the notion of standard fuzzy metric spaces given by J.R. Kider and Z.A. Hussain. In this paper, we study the fundamental…

This paper studies some weighted norm inequalities related to some Calderon-Zygmund singular integrals. Applications to the Sobolev-Gagliardo-Nirenberg inequality, differential forms, and the potential equation du= f are given.

The concept of convexity and its various generalizations is important for quantitative and qualitative studies in operations research or applied mathematics. Recently, E-convex sets and functions were introduced with important implications across…

In this paper, we prove existence, uniqueness stability results for a class of initial value problem for fractional differential equations involving generalized ψ-Hilfer fractional derivative. The result is based on the Banach contraction mapping…
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