On System of Nonlinear Sequential Hybrid Fractional Differential Equations

Abstract

In this study, the existence and uniqueness of the solution for a system consisting of sequential fractional differential equations that contain Caputo–Hadamard (CH) derivative are verified. To study the existence and uniqueness of these solutions, some of the most important results from the fixed point theorems in Banach space were used. A practical example is also given to support the theoretical side that was obtained.

Assessing Impedance Analyzer Data Quality by Fractional Order Calculus: A QCM Sensor Case Study

“…Currently, the basis for a unified and general approach to this complex behavior is the use of fractional order calculus. As the impedance spectroscopy method is generalized, the use of fractional order calculus is required in the modeling of equivalent electrical circuits of complex or nonlinear phenomena [21][22][23]. The development of modern technologies such as supercapacitors [24], fuel cells [25], lithium-ion batteries [26], flyback converters [27], or nanosensors [28] could benefit from new approaches, such as fractional order calculus.…”

Undetermined Coefficients Method for Sequential Fractional Differential Equations

“…Similarly, solutions of impulsive R-L sequential fractional differential equations are studied in [5] and some specific solutions of sequential fractional differential equations with R-L derivatives are investigated in [6]. In [7] and [8], the uniqueness and existence of the solution are proved for sequential fractional differential equations involving the Hadamard derivative and Caputo-Hadamard derivative, respectively. Some existing results are obtained for Caputo-type sequential fractional differential equations with three-point, semi-periodic non-local, and mixed-type boundary conditions [9][10][11].…”