On a Caputo-type fractional derivative respect to another function using a generator by pseudo-operations

This paper studies two efficient numerical methods for the generalized tempered integrodifferential equation with respect to another function. The proposed methods approximate the unknown solution through two phases. First, the backward Euler (BE) method and first-order interpolation quadrature rule are adopted to approximate the temporal derivative and generalized tempered integral term to construct a semi-discrete BE scheme. Second, the backward differentiation formula (BDF) and second-order interpolation quadrature rule are adopted to establish a semi-discrete second-order BDF (BDF2) scheme. Additionally, the stability and convergence of two semi-discrete methods are deduced in detail. To further demonstrate the effectiveness of proposed techniques, fully discrete BE and BDF2 finite difference schemes are formulated. Subsequently, the theoretical results of two fully discrete difference schemes are presented. Finally, the numerical results demonstrate the accuracy and competitiveness of the theoretical analysis.

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Synchronization of generalized fractional complex networks with partial subchannel losses

Dai,

Ma,

Guo

2024

MATH

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<abstract><p>This article focuses on the synchronization problem for two classes of complex networks with subchannel losses and generalized fractional derivatives. Initially, a new stability theorem for generalized fractional nonlinear system is formulated using the properties of generalized fractional calculus and the generalized Laplace transform. This result is also true for classical fractional cases. Subsequently, synchronization criteria for the generalized fractional complex networks are attained by the proposed stability theorem and the state layered method. Lastly, two numerical examples with some new kernel functions are given to validate the synchronization results.</p></abstract>

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On a Caputo-type fractional derivative respect to another function using a generator by pseudo-operations

Cited by 3 publications

References 24 publications

Finite-approximate controllability of impulsive $$\psi -$$Caputo fractional evolution equations with nonlocal conditions

Finite-approximate controllability of impulsive $$\psi -$$Caputo fractional evolution equations with nonlocal conditions

Numerical investigation of generalized tempered-type integrodifferential equations with respect to another function

Synchronization of generalized fractional complex networks with partial subchannel losses

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