Paper Citation Record · LEDGER

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks

As of 8 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2506.07408.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.07408 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:42:39.122698Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy31
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 42f5deb0-02ed-49c1-9b1c-15b2fac978ca · outbound

This paper cites Robust and discriminative image representation: Fractional-order jacobi-fourier moments.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Robust and discriminative image representation: Fractional-order jacobi-fourier moments

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.514308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f591c605-61f1-4523-990e-69659000cd69 · outbound

This paper cites Fractional poisson enhancement model for text detection and recognition in video frames.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional poisson enhancement model for text detection and recognition in video frames

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.504645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cd5dc5fa-abdd-49b3-9100-14e8ae28a9a6 · outbound

This paper cites Image analysis by fractional-order weighted spherical bessel-fourier moments.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Image analysis by fractional-order weighted spherical bessel-fourier moments

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.494962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2826e71c-fd4d-4d5c-82eb-d3285613a766 · outbound

This paper cites Study on fast speed fractional order gradient descent method and its application in neural networks.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Study on fast speed fractional order gradient descent method and its application in neural networks

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.484920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 73a029ed-2a73-471c-a714-a9777dcd084c · outbound

This paper cites Fractional stochastic gradient descent for recommender systems.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional stochastic gradient descent for recommender systems

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.475173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0d3c5212-39a1-408f-b30d-d00bc237534f · outbound

This paper cites Study on fractional order gradient methods.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Study on fractional order gradient methods

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.465196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3cd21983-4a6b-4c17-802f-517c2e133480 · outbound

This paper cites Fractional-order stochastic gradient descent method with momentum and energy for deep neural networks.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional-order stochastic gradient descent method with momentum and energy for deep neural networks

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.455478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 110d65af-f19d-42f0-9b91-7cb315631377 · outbound

This paper cites Variable order fractional gradient descent method and its application in neural networks optimization.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Variable order fractional gradient descent method and its application in neural networks optimization

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.445743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 40f96187-95fe-4daa-9595-654ad5ea457a · outbound

This paper cites A deep learning optimizer based on gr \"u nwald--letnikov fractional order definition.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks A deep learning optimizer based on gr \"u nwald--letnikov fractional order definition

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.435987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5c67807f-d63c-499e-b7cd-0b04fe1baa55 · outbound

This paper cites A fractional-order momentum optimization approach of deep neural networks.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks A fractional-order momentum optimization approach of deep neural networks

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.426487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 259a9a33-749c-4382-93cb-ecc717f83021 · outbound

This paper cites Convolutional neural networks based on fractional-order momentum for parameter training.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Convolutional neural networks based on fractional-order momentum for parameter training

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.416851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ae517f1d-462e-4e72-a705-1b4d14d3f03f · outbound

This paper cites A fractional gradient descent algorithm robust to the initial weights of multilayer perceptron.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks A fractional gradient descent algorithm robust to the initial weights of multilayer perceptron

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.406962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 56cc6c70-974f-4ab8-a4e5-c283a9e9b985 · outbound

This paper cites A comprehensive survey of fractional gradient descent methods and their convergence analysis.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks A comprehensive survey of fractional gradient descent methods and their convergence analysis

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.397139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a340e433-558b-4708-9276-2afaabf9812e · outbound

This paper cites Improved fractional-order gradient descent method based on multilayer perceptron.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Improved fractional-order gradient descent method based on multilayer perceptron

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.387053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7c133d32-86df-437c-b70c-83d86278317c · outbound

This paper cites An adaptive fractional-order bp neural network based on extremal optimization for handwritten digits recognition.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks An adaptive fractional-order bp neural network based on extremal optimization for handwritten digits recognition

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.377297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1c449948-3523-4bce-80d9-77e71d0378b4 · outbound

This paper cites Fractional steepest ascent method for tcu fault detection.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional steepest ascent method for tcu fault detection

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.367354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3b469fd1-52e7-40e6-b8ce-6326695bf990 · outbound

This paper cites Fractional-order convolutional neural networks with population extremal optimization.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional-order convolutional neural networks with population extremal optimization

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.357012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 95cf5dfa-07b5-464d-af9d-564ef3ee5627 · outbound

This paper cites Performance analysis of fractional learning algorithms.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Performance analysis of fractional learning algorithms

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.346660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 56cacbf5-722d-4d88-b137-7fb8f17f9cec · outbound

This paper cites Artificial neural networks: a practical review of applications involving fractional calculus.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Artificial neural networks: a practical review of applications involving fractional calculus

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.335721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 704de5c1-5356-42f0-8787-043b9319b82c · outbound

This paper cites A survey of fractional calculus applications in artificial neural networks.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks A survey of fractional calculus applications in artificial neural networks

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.324302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation de73b643-66ff-4377-9120-ac0a03003c79 · outbound

This paper cites An overview of gradient descent optimization algorithms.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks An overview of gradient descent optimization algorithms

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T05:42:39.066782Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f558d3c-b254-481d-af2e-f0029853d8ba · outbound

This paper cites On the momentum term in gradient descent learning algorithms.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks On the momentum term in gradient descent learning algorithms

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.314161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 05d47749-aa44-495d-bdc5-9922ce13c610 · outbound

This paper cites Nesterov.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Nesterov

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.303624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 58bf9d6f-d58e-4169-a775-d97637836dfb · outbound

This paper cites Two problems with backpropagation and other steepest-descent learning procedures for networks.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Two problems with backpropagation and other steepest-descent learning procedures for networks

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.293246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a19d5662-d3d1-4cbd-89ee-50102a5ed888 · outbound

This paper cites Adaptive subgradient methods for online learning and stochastic optimization.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Adaptive subgradient methods for online learning and stochastic optimization

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T05:42:39.080737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 623ad3de-dcea-4039-a42d-623c8ec11a24 · outbound

This paper cites ADADELTA: An Adaptive Learning Rate Method.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks ADADELTA: An Adaptive Learning Rate Method

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T05:42:39.084136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1283705-3737-4756-8721-c69a641113bb · outbound

This paper cites Lecture 6.5-rmsprop: Divide the gradient by a running average of its recent magnitude.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Lecture 6.5-rmsprop: Divide the gradient by a running average of its recent magnitude

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.276023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8aeb8da4-5dd5-4c69-813c-b567e3c23f84 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Adam: A Method for Stochastic Optimization

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T05:42:39.091315Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f42a6004-a75d-400d-9da0-856af3211757 · outbound

This paper cites SGDR: Stochastic Gradient Descent with Warm Restarts.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks SGDR: Stochastic Gradient Descent with Warm Restarts

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T05:42:39.094689Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2ca110b0-8c3f-474f-aaee-71ca67ad0dbd · outbound

This paper cites A Closer Look at Deep Learning Heuristics: Learning rate restarts, Warmup and Distillation.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks A Closer Look at Deep Learning Heuristics: Learning rate restarts, Warmup and Distillation

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T05:42:39.098437Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b842759-d47d-4c00-a120-4ce443dbf7e8 · outbound

This paper cites Accelerating gradient descent and adam via fractional gradients.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Accelerating gradient descent and adam via fractional gradients

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.265801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f6c0e353-ce38-4348-950f-2b7c06c95fbf · outbound

This paper cites Fractional-order gradient descent learning of bp neural networks with caputo derivative.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional-order gradient descent learning of bp neural networks with caputo derivative

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.255424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6d58e413-ce2c-43f5-aef6-fd175051e292 · outbound

This paper cites Fractional gradient descent algorithms for systems with outliers: A matrix fractional derivative or a scalar fractional derivative.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional gradient descent algorithms for systems with outliers: A matrix fractional derivative or a scalar fractional derivative

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.244228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 89871649-4ed6-4cb1-ad72-313f38cdcd8f · outbound

This paper cites Fractional light gradient boosting machine ensemble learning model: A non-causal fractional difference descent approach.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional light gradient boosting machine ensemble learning model: A non-causal fractional difference descent approach

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.234505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e87ebef7-3cd7-4b31-8116-ce8292318124 · outbound

This paper cites Online public opinion prediction based on rolling fractional grey model with new information priority.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Online public opinion prediction based on rolling fractional grey model with new information priority

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.223749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5fe93704-634b-4801-a639-2d4b8f256ef1 · outbound

This paper cites Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.213606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 03bbcfa3-5408-4e6b-8cd6-2eb8c3e718c9 · outbound

This paper cites Fractional-order gradient approach for optimizing neural networks: A theoretical and empirical analysis.

Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks Fractional-order gradient approach for optimizing neural networks: A theoretical and empirical analysis

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:42:39.202414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.