{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T16:12:59Z","timestamp":1783008779497,"version":"3.54.5"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"13","license":[{"start":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T00:00:00Z","timestamp":1717113600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T00:00:00Z","timestamp":1717113600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Multimed Tools Appl"],"DOI":"10.1007\/s11042-024-19440-0","type":"journal-article","created":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T06:01:53Z","timestamp":1717135313000},"page":"12329-12345","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Edge detection using the Prewitt operator with fractional order telegraph partial differential equations (PreFOTPDE)"],"prefix":"10.1007","volume":"84","author":[{"given":"Mehmet Emin","family":"Tenekeci","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4515-1585","authenticated-orcid":false,"given":"Sadeq Taha","family":"Abdulazeez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kerim","family":"Karada\u011f","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mahmut","family":"Modanli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,5,31]]},"reference":[{"issue":"3","key":"19440_CR1","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1063\/1.369258","volume":"85","author":"PM Jordan","year":"1999","unstructured":"Jordan PM, Puri A (1999) Digital signal propagation in dispersive media. J Appl Phys 85(3):1273\u20131282","journal-title":"J Appl Phys"},{"key":"19440_CR2","doi-asserted-by":"publisher","first-page":"789","DOI":"10.1088\/0266-5611\/9\/6\/013","volume":"9","author":"VH Weston","year":"1993","unstructured":"Weston VH, He S (1993) Wave splitting of telegraph equation in R3 and its applications to inverse scattering. Inverse Probl 9:789\u2013812","journal-title":"Inverse Probl"},{"issue":"1","key":"19440_CR3","first-page":"9","volume":"11","author":"J Banasiak","year":"1998","unstructured":"Banasiak J, Mika JR (1998) Singularly perturbed telegraph equations with applications in the random walk theory. J Appl Math Stoch Anal 11(1):9\u201328","journal-title":"J Appl Math Stoch Anal"},{"issue":"2","key":"19440_CR4","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/BF01045166","volume":"3","author":"A Janssen","year":"1990","unstructured":"Janssen A (1990) The distance between the Kac process and the Wiener process with applications to generalized telegraph equations. J Theor Probab 3(2):349\u2013360","journal-title":"J Theor Probab"},{"key":"19440_CR5","unstructured":"I. Podlubny, Fractional Differential Equations, Math. Sci. Eng., New York, Academic Press, 1999."},{"key":"19440_CR6","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1016\/j.mcm.2008.09.011","volume":"49","author":"MP Lazarevic","year":"2009","unstructured":"Lazarevic MP, Spasic AM (2009) Finite-time stability analysis of fractional-order time-delay systems: gronwalls approach. Math Comput Model 49:475\u2013481","journal-title":"Math Comput Model"},{"key":"19440_CR7","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.optcom.2015.05.019","volume":"353","author":"X Liu","year":"2015","unstructured":"Liu X, Fang S (2015) A convenient and robust edge detection method based on ant colony optimization. Opt Commun 353:147\u2013157","journal-title":"Opt Commun"},{"issue":"4","key":"19440_CR8","doi-asserted-by":"publisher","first-page":"957","DOI":"10.31577\/cai_2022_4_957","volume":"41","author":"LI Mochurad","year":"2022","unstructured":"Mochurad LI (2022) Canny edge detection analysis based on parallel algorithm, constructed complexity scale and CUDA. Computing and Informatics 41(4):957\u2013980","journal-title":"Computing and Informatics"},{"issue":"6","key":"19440_CR9","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1016\/j.jare.2016.04.002","volume":"7","author":"S Thirumavalavan","year":"2016","unstructured":"Thirumavalavan S, Jayaraman S (2016) An improved teaching\u2013learning based robust edge detection algorithm for noisy images. J Adv Res 7(6):979\u2013989","journal-title":"J Adv Res"},{"key":"19440_CR10","doi-asserted-by":"crossref","unstructured":"Neto CMS, Costa FB, Barreto RL, Rocha TOA, Ribeiro RLA (2013) \"Wavelet-based method for detection of electrical and electromechanical oscillations in synchronous generators,\" In: 2013 Brazilian Power Electronics Conference, pp 699\u2013704","DOI":"10.1109\/COBEP.2013.6785191"},{"key":"19440_CR11","doi-asserted-by":"crossref","unstructured":"Balochian, S., & Baloochian, H. (2022). Edge detection on noisy images using Prewitt operator and fractional order differentiation. Multimedia Tools and Applications, 1\u201312.","DOI":"10.1007\/s11042-022-12011-1"},{"key":"19440_CR12","doi-asserted-by":"crossref","unstructured":"Hagara, M., & Kubinec, P. (2018). About Edge Detection in Digital Images.\u00a0Radioengineering,\u00a027(4).","DOI":"10.13164\/re.2018.0919"},{"key":"19440_CR13","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/j.neucom.2022.06.083","volume":"503","author":"J Jing","year":"2022","unstructured":"Jing J, Liu S, Wang G, Zhang W, Sun C (2022) Recent advances on image edge detection: A comprehensive review. Neurocomputing 503:259\u2013271","journal-title":"Neurocomputing"},{"key":"19440_CR14","doi-asserted-by":"publisher","first-page":"107280","DOI":"10.1016\/j.sigpro.2019.107280","volume":"167","author":"SM Ismail","year":"2020","unstructured":"Ismail SM, Said LA, Radwan AG, Madian AH, Abu-ElYazeed MF (2020) A novel image encryption system merging fractional-order edge detection and generalized chaotic maps. Signal Process 167:107280","journal-title":"Signal Process"},{"key":"19440_CR15","doi-asserted-by":"publisher","first-page":"107852","DOI":"10.1016\/j.sigpro.2020.107852","volume":"180","author":"K Kaur","year":"2021","unstructured":"Kaur K, Jindal N, Singh K (2021) Fractional Fourier Transform based Riesz fractional derivative approach for edge detection and its application in image enhancement. Signal Process 180:107852","journal-title":"Signal Process"},{"key":"19440_CR16","doi-asserted-by":"crossref","unstructured":"Sadykova, D., & James, A. P. (2017, September). Quality assessment metrics for edge detection and edge-aware filtering: A tutorial review. In 2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI) (pp. 2366\u20132369). IEEE.","DOI":"10.1109\/ICACCI.2017.8126200"},{"issue":"12","key":"19440_CR17","first-page":"52","volume":"30","author":"A Abirami","year":"2023","unstructured":"Abirami A, Prakash P (2023) Fractional Diffusion Equation for Medical Image Denoising using ADI Scheme. J Popul Ther Clin Pharmacol 30(12):52\u201363","journal-title":"J Popul Ther Clin Pharmacol"},{"key":"19440_CR18","doi-asserted-by":"crossref","unstructured":"Zhang, R., Zhao, F., Dai, F., & Shi, Y. (2020, October). Algorithm for Fog-degraded Image Enhancement Based on Adaptive Fractional-order PDE. In 2020 IEEE 5th International Conference on Signal and Image Processing (ICSIP) (pp. 129\u2013135). IEEE.","DOI":"10.1109\/ICSIP49896.2020.9339311"},{"issue":"14","key":"19440_CR19","doi-asserted-by":"publisher","first-page":"4255","DOI":"10.1080\/10106049.2021.1882007","volume":"37","author":"LT Pham","year":"2022","unstructured":"Pham LT, Oksum E, Le DV, Ferreira FJ, Le ST (2022) Edge detection of potential field sources using the softsign function. Geocarto Int 37(14):4255\u20134268","journal-title":"Geocarto Int"},{"issue":"1","key":"19440_CR20","doi-asserted-by":"publisher","first-page":"64","DOI":"10.3390\/fractalfract7010064","volume":"7","author":"X Bai","year":"2023","unstructured":"Bai X, Zhang D, Shi S, Yao W, Guo Z, Sun J (2023) A fractional-order telegraph diffusion model for restoring texture images with multiplicative noise. Fractal and Fractional 7(1):64","journal-title":"Fractal and Fractional"},{"key":"19440_CR21","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.cnsns.2018.01.020","volume":"61","author":"JM Cruz-Duarte","year":"2018","unstructured":"Cruz-Duarte JM, Rosales-Garcia J, Correa-Cely CR, Garcia-Perez A, Avina-Cervantes JG (2018) A closed form expression for the Gaussian\u2013based Caputo-Fabrizio fractional derivative for signal processing applications. Commun Nonlinear Sci Numer Simul 61:138\u2013148","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"19440_CR22","doi-asserted-by":"publisher","first-page":"101883","DOI":"10.1016\/j.bspc.2020.101883","volume":"59","author":"AK Shukla","year":"2020","unstructured":"Shukla AK, Pandey RK, Pachori RB (2020) A fractional filter based efficient algorithm for retinal blood vessel segmentation. Biomed Signal Process Control 59:101883","journal-title":"Biomed Signal Process Control"},{"key":"19440_CR23","doi-asserted-by":"publisher","first-page":"101584","DOI":"10.1016\/j.bspc.2019.101584","volume":"54","author":"JE Sol\u00eds-P\u00e9rez","year":"2019","unstructured":"Sol\u00eds-P\u00e9rez JE, G\u00f3mez-Aguilar JF, Escobar-Jim\u00e9nez RF, Reyes-Reyes J (2019) Blood vessel detection based on fractional Hessian matrix with non-singular Mittag-Leffler Gaussian kernel. Biomed Signal Process Control 54:101584","journal-title":"Biomed Signal Process Control"},{"key":"19440_CR24","doi-asserted-by":"crossref","unstructured":"Chandra, S. K., & Bajpai, M. K. (2018, October). Effective algorithm for benign brain tumor detection using fractional calculus. In TENCON 2018\u20132018 IEEE Region 10 Conference (pp. 2408\u20132413). IEEE.","DOI":"10.1109\/TENCON.2018.8650163"},{"key":"19440_CR25","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1016\/j.sigpro.2014.06.004","volume":"107","author":"HA Jalab","year":"2015","unstructured":"Jalab HA, Ibrahim RW (2015) Fractional Alexander polynomials for image denoising. Signal Process 107:340\u2013354","journal-title":"Signal Process"},{"issue":"1","key":"19440_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-020-02890-9","volume":"2020","author":"B Ghanbari","year":"2020","unstructured":"Ghanbari B, Atangana A (2020) Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels. Adv Difference Equ 2020(1):1\u201319","journal-title":"Adv Difference Equ"},{"issue":"1","key":"19440_CR27","doi-asserted-by":"publisher","first-page":"172","DOI":"10.21037\/qims-21-15","volume":"12","author":"RW Ibrahim","year":"2022","unstructured":"Ibrahim RW, Jalab HA, Karim FK, Alabdulkreem E, Ayub MN (2022) A medical image enhancement based on generalized class of fractional partial differential equations. Quant Imaging Med Surg 12(1):172","journal-title":"Quant Imaging Med Surg"},{"issue":"3","key":"19440_CR28","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1007\/s00034-019-01200-3","volume":"39","author":"JE Lav\u00edn-Delgado","year":"2020","unstructured":"Lav\u00edn-Delgado JE, Sol\u00eds-P\u00e9rez JE, G\u00f3mez-Aguilar JF, Escobar-Jim\u00e9nez RF (2020) A new fractional-order mask for image edge detection based on Caputo-Fabrizio fractional-order derivative without singular kernel. Circuits Systems Signal Process 39(3):1419\u20131448","journal-title":"Circuits Systems Signal Process"},{"key":"19440_CR29","doi-asserted-by":"publisher","first-page":"164507","DOI":"10.1016\/j.ijleo.2020.164507","volume":"218","author":"CY Ma","year":"2020","unstructured":"Ma CY, Shiri B, Wu GC, Baleanu D (2020) New fractional signal smoothing equations with short memory and variable order. Optik 218:164507","journal-title":"Optik"},{"key":"19440_CR30","doi-asserted-by":"publisher","first-page":"109463","DOI":"10.1016\/j.chaos.2019.109463","volume":"131","author":"Q Wang","year":"2020","unstructured":"Wang Q, Ma J, Yu S, Tan L (2020) Noise detection and image denoising based on fractional calculus. Chaos, Solitons Fractals 131:109463","journal-title":"Chaos, Solitons Fractals"},{"issue":"4","key":"19440_CR31","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1007\/s40815-020-01030-5","volume":"23","author":"M Versaci","year":"2021","unstructured":"Versaci M, Morabito FC (2021) Image edge detection: A new approach based on fuzzy entropy and fuzzy divergence. Int J Fuzzy Syst 23(4):918\u2013936","journal-title":"Int J Fuzzy Syst"},{"issue":"10","key":"19440_CR32","doi-asserted-by":"publisher","first-page":"6642","DOI":"10.1109\/TCSVT.2022.3177320","volume":"32","author":"L Yan","year":"2022","unstructured":"Yan L, Ma S, Wang Q, Chen Y, Zhang X, Savakis A, Liu D (2022) Video captioning using global-local representation. IEEE Trans Circuits Syst Video Technol 32(10):6642\u20136656","journal-title":"IEEE Trans Circuits Syst Video Technol"},{"issue":"1","key":"19440_CR33","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1109\/TCSVT.2022.3202574","volume":"33","author":"L Yan","year":"2022","unstructured":"Yan L, Wang Q, Ma S, Wang J, Yu C (2022) Solve the puzzle of instance segmentation in videos: A weakly supervised framework with spatio-temporal collaboration. IEEE Trans Circuits Syst Video Technol 33(1):393\u2013406","journal-title":"IEEE Trans Circuits Syst Video Technol"},{"key":"19440_CR34","doi-asserted-by":"publisher","first-page":"101975","DOI":"10.1016\/j.compenvurbsys.2023.101975","volume":"103","author":"F Guan","year":"2023","unstructured":"Guan F, Fang Z, Zhang X, Zhong H, Zhang J, Huang H (2023) Using street-view panoramas to model the decision-making complexity of road intersections based on the passing branches during navigation. Comput Environ Urban Syst 103:101975","journal-title":"Comput Environ Urban Syst"},{"issue":"6","key":"19440_CR35","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1109\/TPAMI.1986.4767851","volume":"8","author":"J Canny","year":"1986","unstructured":"Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 8(6):679\u2013698","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"19440_CR36","first-page":"19","volume":"96","author":"SA Ahmed","year":"2018","unstructured":"Ahmed SA (2018) Comparat\u0131ve Study Among Sobel, Prew\u0131tt and Canny Edge Detect\u0131on Operators Used In Image Process\u0131ng. Journal of Theoretical and Applied Information Technology 96:19","journal-title":"Journal of Theoretical and Applied Information Technology"},{"issue":"6","key":"19440_CR37","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1515\/ijnsns-2019-0300","volume":"22","author":"K Srinivasa","year":"2021","unstructured":"Srinivasa K, Rezazadeh H (2021) Numerical solution for the fractional-order one-dimensional telegraph equation via wavelet technique. International Journal of Nonlinear Sciences and Numerical Simulation 22(6):767\u2013780","journal-title":"International Journal of Nonlinear Sciences and Numerical Simulation"},{"issue":"2","key":"19440_CR38","first-page":"162","volume":"19","author":"NH Sweilam","year":"2020","unstructured":"Sweilam NH, Nagy AM, El-Sayed AA (2020) Sinc-Chebyshev collocation method for time-fractional order telegraph equation. Appl Comput Math 19(2):162\u2013174","journal-title":"Appl Comput Math"},{"issue":"1","key":"19440_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1687-1847-2012-204","volume":"2012","author":"Y Khan","year":"2012","unstructured":"Khan Y, Dibl\u00edk J, Faraz N, \u0160marda Z (2012) An efficient new perturbative Laplace method for space-time fractional telegraph equations. Adv Difference Equ 2012(1):1\u20139","journal-title":"Adv Difference Equ"},{"issue":"1","key":"19440_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-018-1789-2","volume":"2018","author":"M Modanl\u0131","year":"2018","unstructured":"Modanl\u0131 M (2018) Two numerical methods for fractional partial differential equation with nonlocal boundary value problem. Adv Difference Equ 2018(1):1\u201319","journal-title":"Adv Difference Equ"},{"issue":"9","key":"19440_CR41","first-page":"1319","volume":"51","author":"P YiFei","year":"2008","unstructured":"YiFei P, WeiXing W, JiLiu Z, YiYang W, HuaDing J (2008) Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation. Sci China Ser F: Inf Sci 51(9):1319\u20131339","journal-title":"Sci China Ser F: Inf Sci"},{"key":"19440_CR42","doi-asserted-by":"publisher","first-page":"7407","DOI":"10.1007\/s11042-015-2663-9","volume":"75","author":"A Attar","year":"2016","unstructured":"Attar A, Shahbahrami A, Rad RM (2016) Image quality assessment using edge based features. Multimedia tools and applications 75:7407\u20137422","journal-title":"Multimedia tools and applications"},{"key":"19440_CR43","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.patcog.2016.10.008","volume":"63","author":"W Zhang","year":"2017","unstructured":"Zhang W, Zhao Y, Breckon TP, Chen L (2017) Noise robust image edge detection based upon the automatic anisotropic Gaussian kernels. Pattern Recogn 63:193\u2013205","journal-title":"Pattern Recogn"},{"key":"19440_CR44","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.optcom.2015.05.019","volume":"353","author":"X Liu","year":"2015","unstructured":"Liu X, Fang S (2015) A convenient and robust edge detection method based on ant colony optimization. Optics Communications 353:147\u2013157","journal-title":"Optics Communications"}],"container-title":["Multimedia Tools and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11042-024-19440-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11042-024-19440-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11042-024-19440-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T03:28:54Z","timestamp":1746156534000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11042-024-19440-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,31]]},"references-count":44,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["19440"],"URL":"https:\/\/doi.org\/10.1007\/s11042-024-19440-0","relation":{},"ISSN":["1573-7721"],"issn-type":[{"value":"1573-7721","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,31]]},"assertion":[{"value":"19 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 May 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 May 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This work was completed under ethical compliance.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"The authors affirm that they have no conflicts of interest.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of \u0131nterest"}}]}}