On existence theorems for some generalized nonlinear functional-integral equations with applications

Mishra, Lakshmi Narayan; Sen, Mausumi; Mohapatra, R. N.

doi:10.2298/fil1707081n

Cited by 28 publications

(4 citation statements)

References 23 publications

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“…11, No. 10;2017 divided to three parts, training data, validation data and test data to a percent of 4:1:1 in order to achieve optimal. Final test sequence is used to test the trained model.…”

Section: Resultsmentioning

confidence: 99%

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Relative Pose of IMU-Camera Calibration Based on BP Network

Guo

Fang³

et al. 2017

MAS

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There are many applications of the combination of IMU (Inertial Measurements Unit) and camera in fields of electronic image stabilization, enhancement reality and navigation where camera-IMU relative pose calibration is one of the key technologies, which may effectively avoid the cases of insufficient feature points, unclear texture, blurred image, etc. In this paper, a new camera-IMU relative pose calibration method is proposed by establishing a BP neural network model. Thus we can obtain the transform from IMU inertial measurements to images and achieve camera-IMU relative pose calibration. The advantage of our method is the application of BP neural network using Levenberg-Marquardt algorithm, avoiding more complex calculations for the whole process. And it is convient for the application of camera-IMU combination system. Meanwhile, nonlinearities and noises are compensated while training and the impact of gravity can be ignored. Our experimental results demonstrated that this method can achieve camera-IMU relative pose calibration and the accuracy of quaternion estimation has reached about 0.01.

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Section: Resultsmentioning

confidence: 99%

“…Mishra, 2017;Deepmala, 2014) of the weights.4 Here, we employ Levenberg-Marquardt algorithm, i.e. with a gradient seeking maximum (minimum) value of the algorithm to find a set of optimal parameters vector to minimum value function, which compromises the Newton method and gradient method.…”

Section: Alogorithmmentioning

confidence: 99%

Relative Pose of IMU-Camera Calibration Based on BP Network

Guo

Fang³

et al. 2017

MAS

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“…It is worthwhile mentioning that Erdélyi-Kober integrals are applied to describe processes with continuously distributed scaling, medium with noninteger mass dimension, modeling of viscoelastic materials, and advection and dispersion of solutes in porous media. Quadratic integral equations have many potential applications in describing a great number of events, and problems of the real world, that can benefit both the understanding of profound complexities in the application and the field of fractional calculus itself [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

On the solvability of a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator

Pathak

Mishra

2023

Math Methods in App Sciences

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In this paper, utilizing the technique of generalized Darbo's fixed‐point theorem associated with measure of noncompactness in Banach space, we analyze the existence of solution for a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator. The existing result was obtained to strengthen the ones mentioned previously in the literature. An example for a class of nonlinear functional integral equations is also presented to validate our main result. Finally, we propose the numerical method formed by the modified homotopy perturbation approach to resolving the problem with acceptable accuracy.

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“…[2] In the twentieth century, the theory of Nonlinear functional integral equations has become an active area of research due to their applications in the fields such as engineering, mechanics, physics, chemistry, biology, economics and so on. For more details, one can see [3,4,5,6,7,8,9], and references therein.…”

Section: Introductionmentioning

confidence: 99%