Nonlinear Differential Equations Analysis

Our first main purpose is to establish a framework for initial value problems for time-fractional evolution equation of order $α\in (0,1)$ in Banach space $X$: $$ \pppa (u(t)-a) = Au(t) + F(t), \quad 0

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Bu çalışmada, her iki ucundan düzgün yayılı eksenel basınç kuvveti etkisindeki piezoelektrik silindirin Çin feneri tipi stabilite kaybı problemleri lineer olmayan elektroelastisite teorisinin üç boyutlu kesin denklemleri yardımıyla eksenel simetrik durum için modellenmiştir. Bu problemlerin çözümü, detayları [1]’de ve…

In this study, the regular trace formula of the differential operator defined by a two-order differential equation and antiperiodic boundary conditions over a finite interval is obtained. Knowledge of regular trace formulas is a well-known tool in calculating the initial eigenvalues of boundary value problems and in s…

We consider the concept of a $ t $ -basis generated by the tensor product of Banach spaces. We introduce the concept of a $ * $ -harmonic Banach-valued ( $ X $ -valued) function, where the space $ X $ under consideration has an involution $ * $ . Using the fact that the classical system of exponentials forms a $ t $ -…

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In this study, we introduce some properties of the Sturm-Liouville boundary value problem on bounded time scales. Then, to give the solution of inverse problems, uniqueness theorems are provided for two characteristic data: the Weyl function and a set of j-th eigenvalues of countably infinite Sturm-Liouville boundary…

This paper is devoted to the explicit representation of solutions for a class of differential equations involving the Caputo–Fabrizio fractional derivative with a nonsingular kernel. Motivated by the lack of explicit representation formulas for Caputo–Fabrizio fractional systems in the existing literature, two distinc…

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In this article we study local classical solvability and continuous dependence for a class of semilinear nonlocal pseudo-differential evolution equations in $ \mathbb{R}^N $. The spatial operator combines the analytic power multiplier $ (I-\Delta e^{-b\Delta})^{s/2} $ with the Euclidean bosonic heat multiplier $ -\Del…

In this paper, the existence of solutions to Caputo–Hadamard fractional differential equations is investigated using measures of noncompactness and the Petryshyn fixed point theorem. Several new results are established, recovering certain earlier results under weaker conditions. Finally, two illustrative examples are…

Abstract This study addresses the exponential stabilization of second-order impulsive delay differential equations and impulsive integro-delay differential equations with finitely many constant delays via Lyapunov–Krasovskii functionals. Throughout the paper, four new theorems are established, providing sufficient con…