{"cited_by_count":1204975,"description":"This cluster of papers focuses on the modeling, analysis, and applications of anomalous diffusion using fractional calculus, nonlinear equations, and the homotopy analysis method. It explores phenomena such as random walk, fractional derivatives, time-fractional diffusion equations, single particle tracking in biological cells, and diffusion in crowded environments.","display_name":"Fractional Differential Equations Solutions","domain_id":"3","external_ids":{"openalex":"https://openalex.org/T10288","wikipedia":"https://en.wikipedia.org/wiki/Anomalous_diffusion"},"field_id":"26","id":"T10288","keywords":[{"display_name":"Caputo fractional derivative","id":"caputo-fractional-derivative","score":0.5062,"url":"https://openalex.org/keywords/caputo-fractional-derivative"},{"display_name":"fractional differential equations","id":"fractional-differential-equations","score":0.4443,"url":"https://openalex.org/keywords/fractional-differential-equations"},{"display_name":"fractional calculus","id":"fractional-calculus","score":0.3807,"url":"https://openalex.org/keywords/fractional-calculus"},{"display_name":"fractional derivatives","id":"fractional-derivatives","score":0.436,"url":"https://openalex.org/keywords/fractional-derivatives"},{"display_name":"anomalous diffusion","id":"anomalous-diffusion","score":0.3677,"url":"https://openalex.org/keywords/anomalous-diffusion"},{"display_name":"Adomian decomposition method","id":"adomian-decomposition-method","score":0.4426,"url":"https://openalex.org/keywords/adomian-decomposition-method"},{"display_name":"homotopy perturbation method","id":"homotopy-perturbation-method","score":0.4853,"url":"https://openalex.org/keywords/homotopy-perturbation-method"},{"display_name":"Riemann-Liouville fractional derivative","id":"riemann-liouville-fractional-derivative","score":0.451,"url":"https://openalex.org/keywords/riemann-liouville-fractional-derivative"},{"display_name":"fractional partial differential equations","id":"fractional-partial-differential-equations","score":0.6973,"url":"https://openalex.org/keywords/fractional-partial-differential-equations"},{"display_name":"subdiffusion","id":"subdiffusion","score":0.4014,"url":"https://openalex.org/keywords/subdiffusion"},{"display_name":"Mittag-Leffler function","id":"mittag-leffler-function","score":0.4283,"url":"https://openalex.org/keywords/mittag-leffler-function"},{"display_name":"nonlinear fractional differential equations","id":"nonlinear-fractional-differential-equations","score":0.4114,"url":"https://openalex.org/keywords/nonlinear-fractional-differential-equations"},{"display_name":"homotopy analysis method","id":"homotopy-analysis-method","score":0.306,"url":"https://openalex.org/keywords/homotopy-analysis-method"},{"display_name":"variational iteration method","id":"variational-iteration-method","score":0.4745,"url":"https://openalex.org/keywords/variational-iteration-method"},{"display_name":"fractional diffusion equation","id":"fractional-diffusion-equation","score":0.6885,"url":"https://openalex.org/keywords/fractional-diffusion-equation"},{"display_name":"continuous time random walk","id":"continuous-time-random-walk","score":0.3792,"url":"https://openalex.org/keywords/continuous-time-random-walk"},{"display_name":"fractional integrals","id":"fractional-integrals","score":0.3378,"url":"https://openalex.org/keywords/fractional-integrals"},{"display_name":"time-fractional derivative","id":"time-fractional-derivative","score":0.6205,"url":"https://openalex.org/keywords/time-fractional-derivative"},{"display_name":"Caputo-Fabrizio derivative","id":"caputo-fabrizio-fractional-derivative","score":0.5492,"url":"https://openalex.org/keywords/caputo-fabrizio-fractional-derivative"},{"display_name":"conformable fractional derivative","id":"conformable-fractional-derivative","score":0.4015,"url":"https://openalex.org/keywords/conformable-fractional-derivative"},{"display_name":"superdiffusion","id":"superdiffusion","score":0.2464,"url":"https://openalex.org/keywords/superdiffusion"},{"display_name":"operational matrices","id":"operational-matrix","score":0.5193,"url":"https://openalex.org/keywords/operational-matrix"},{"display_name":"numerical solution of fractional differential equations","id":"numerical-solution-of-fractional-differential-equations","score":0.8335,"url":"https://openalex.org/keywords/numerical-solution-of-fractional-differential-equations"},{"display_name":"fractional diffusion","id":"fractional-diffusion","score":0.4935,"url":"https://openalex.org/keywords/fractional-diffusion"},{"display_name":"Atangana-Baleanu derivative","id":"atangana-baleanu-fractional-derivative","score":0.4825,"url":"https://openalex.org/keywords/atangana-baleanu-fractional-derivative"}],"legacy_keywords":["Anomalous Diffusion","Fractional Calculus","Nonlinear Equations","Homotopy Analysis Method","Random Walk","Fractional Derivatives","Time-Fractional Diffusion Equation","Single Particle Tracking","Biological Cells","Crowded Environments"],"openalex_id":"https://openalex.org/T10288","source_created_date":"2024-01-23T15:27:05","source_updated_date":"2026-10-17T03:02:00","subfield_id":"2611","url":"/topics/T10288","works_api_url":"https://api.openalex.org/works?filter=topics.id:T10288","works_count":55539,"label":"Fractional Differential Equations Solutions","provider":"openalex","revision":"ef8e3a0213f4cda6","taxonomy_revision":"f050b5d4780b1289","title":"Fractional Differential Equations Solutions","kind":"topic-directory","aeo_cohort":"topic-directory","catalogue_revision":"f050b5d4780b1289","numeric_address":"36240178142912629","address_version":"morton4x16-v1","coordinates":[3,26,2611,10288],"answer_status":"Directory metadata; local answer requires separate source review","truth_status":"Subject descriptor, not a factual answer or a demonstrated knowledge gap","reviewed_answer":null}