On nonlinear coupled evolution system with nonlocal subsidiary conditions under fractal‐fractional order derivative

Abstract

In the given paper, we develop and extend a qualitative analysis of a novel nonlinear system of fractional pantograph evolution differential equations (FPEDEs) involving fractal-fractional derivative in Atangana-Baleanu sense. To discuss the proposed problem, we establish the essential conditions for the existence and uniqueness results. The used arguments for the analysis are the fixed point techniques of Banach and Krasnoselskii. Moreover, the Ulam-Hyers stability of solutions for the system at hand is discussed. Two interesting pertinent examples are presented.

Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function

“…In this section, we provide some qualitative analyses of the ψ-piecewise Caputo pantograph FDE (6). First, certain crucial results are provided for the benefit of the upcoming analysis.…”

“…Many classes of fractional differential equations (FDEs) have been extensively studied and analyzed in the past decades; for example, theories involving the existence of unique solutions have been documented [5][6][7][8][9][10]. Numerical and analytical methods have been developed with the aim of solving such equations [11][12][13][14].…”

Sequential fractional pantograph differential equations with nonlocal boundary conditions: Uniqueness and Ulam-Hyers-Rassias stability

“…Dierential equations of arbitrary order have recently been studied by many researchers, these equations will be used to describe phenomena of real world problems. For more details, see the works [2,14,21,27] and the references therein. Many interesting and important area concerning of research for dierential equations with fractional calculus are devoted to the existence theory and stability analysis of the solutions, for instance, for instance, see papers [4,7,9,12,17,24].…”

Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

“…To overcome this challenges, these kinds of phenomena can be given the assistance of coupled systems of DEs. As of late, coupled systems of FDEs have been investigated with various methodologies, see [6][7][8][9][10].…”