id sid eid entity type cana-4595 1 1 1074 CARDINAL cana-4595 1 2 32 CARDINAL cana-4595 2 1 9s CARDINAL cana-4595 2 2 2025 DATE cana-4595 3 1 2969 CARDINAL cana-4595 4 1 anil kumar1* PERSON cana-4595 5 1 rohilkhand university ORG cana-4595 5 2 bareilly GPE cana-4595 5 3 2assistant ORG cana-4595 5 4 rohilkhand university ORG cana-4595 5 5 bareilly GPE cana-4595 6 1 12-01-2025 CARDINAL cana-4595 6 2 15-02-2025 CARDINAL cana-4595 6 3 01-03-2025 CARDINAL cana-4595 7 1 legendre ORG cana-4595 7 2 chebyshev GPE cana-4595 7 3 jacobi ORG cana-4595 13 1 non-linear ORG cana-4595 16 1 gnocchi polynomials ORG cana-4595 16 2 non-linear ORG cana-4595 17 1 1 CARDINAL cana-4595 19 1 the past couple of years DATE cana-4595 19 2 1 CARDINAL cana-4595 22 1 1 CARDINAL cana-4595 23 1 β€’ CARDINAL cana-4595 23 2 riemann-liouville fractional derivative 𝑅𝐿𝐷𝛼𝑓(π‘₯ ORG cana-4595 23 3 1 CARDINAL cana-4595 23 4 0 CARDINAL cana-4595 24 1 1074 CARDINAL cana-4595 24 2 32 CARDINAL cana-4595 25 1 9s CARDINAL cana-4595 25 2 2025 DATE cana-4595 25 3 2970 CARDINAL cana-4595 26 1 β€’ CARDINAL cana-4595 26 2 1 CARDINAL cana-4595 27 1 0 CARDINAL cana-4595 29 1 2 CARDINAL cana-4595 29 2 2 CARDINAL cana-4595 31 1 2𝑛 + 1)π‘₯𝐺𝑛(π‘₯ DATE cana-4595 31 2 1 CARDINAL cana-4595 32 1 3 CARDINAL cana-4595 36 1 𝑐𝑛]𝑇 NORP cana-4595 37 1 3 CARDINAL cana-4595 37 2 legendre ORG cana-4595 37 3 4 CARDINAL cana-4595 38 1 β€’ CARDINAL cana-4595 39 1 β€’ CARDINAL cana-4595 40 1 non-linear ORG cana-4595 42 1 2 CARDINAL cana-4595 42 2 2.1 CARDINAL cana-4595 44 1 5 CARDINAL cana-4595 45 1 riemann-liouville ORG cana-4595 45 2 caputo PERSON cana-4595 46 1 2.1.1 CARDINAL cana-4595 46 2 0 CARDINAL cana-4595 46 3 riemann-liouville ORG cana-4595 47 1 0 CARDINAL cana-4595 48 1 1074 CARDINAL cana-4595 48 2 32 CARDINAL cana-4595 49 1 9s CARDINAL cana-4595 49 2 2025 DATE cana-4595 50 1 0 CARDINAL cana-4595 50 2 6 CARDINAL cana-4595 51 1 2.1.2 CARDINAL cana-4595 51 2 three CARDINAL cana-4595 51 3 1 CARDINAL cana-4595 51 4 riemann-liouville ORG cana-4595 51 5 riemann-liouville ORG cana-4595 52 1 1 CARDINAL cana-4595 53 1 0 CARDINAL cana-4595 54 1 7 CARDINAL cana-4595 55 1 2 CARDINAL cana-4595 55 2 riemann-liouville ORG cana-4595 55 3 1 CARDINAL cana-4595 56 1 0 CARDINAL cana-4595 57 1 riemann-liouville ORG cana-4595 57 2 8 CARDINAL cana-4595 58 1 3 CARDINAL cana-4595 58 2 grΓΌnwald-letnikov ORG cana-4595 59 1 9 CARDINAL cana-4595 60 1 2.1.3 CARDINAL cana-4595 60 2 β€’ CARDINAL cana-4595 60 3 𝑓(π‘₯ PERSON cana-4595 60 4 𝐷𝛼(π‘Žπ‘“(π‘₯ PERSON cana-4595 62 1 + 𝑏𝐷𝛼𝑔(π‘₯ PERSON cana-4595 62 2 β€’ CARDINAL cana-4595 62 3 two CARDINAL cana-4595 62 4 β€’ CARDINAL cana-4595 62 5 𝐷𝛼π‘₯𝑝 PERSON cana-4595 62 6 + 1 DATE cana-4595 63 1 2.2 CARDINAL cana-4595 63 2 2.2.1 CARDINAL cana-4595 63 3 1074 CARDINAL cana-4595 63 4 32 CARDINAL cana-4595 64 1 9s CARDINAL cana-4595 64 2 2025 DATE cana-4595 64 3 2972 CARDINAL cana-4595 65 1 2𝑛 + 1)π‘₯𝐺𝑛(π‘₯ DATE cana-4595 65 2 1 CARDINAL cana-4595 66 1 10 CARDINAL cana-4595 67 1 2.2.2 CARDINAL cana-4595 68 1 2.3 CARDINAL cana-4595 68 2 2.3.1 CARDINAL cana-4595 72 1 11 CARDINAL cana-4595 73 1 2.3.2 CARDINAL cana-4595 73 2 β€’ CARDINAL cana-4595 74 1 β€’ CARDINAL cana-4595 75 1 β€’ CARDINAL cana-4595 78 1 3 CARDINAL cana-4595 78 2 3.1 CARDINAL cana-4595 78 3 3.1.1 CARDINAL cana-4595 81 1 𝐷𝛼 to 𝑓(π‘₯ PERSON cana-4595 82 1 1074 CARDINAL cana-4595 82 2 32 CARDINAL cana-4595 83 1 9s CARDINAL cana-4595 83 2 2025 DATE cana-4595 83 3 2973 CARDINAL cana-4595 83 4 𝐷𝛼𝐺(π‘₯ PERSON cana-4595 83 5 𝐷𝛼 to 𝑓(π‘₯ PERSON cana-4595 85 1 𝑐𝑛]𝑇 ORG cana-4595 88 1 𝑃𝑛,π‘š PRODUCT cana-4595 88 2 𝑝0,0 ORG cana-4595 90 1 𝑝2,2 PERSON cana-4595 90 2 1 CARDINAL cana-4595 92 1 3.2 CARDINAL cana-4595 92 2 3.2.1 CARDINAL cana-4595 92 3 zero CARDINAL cana-4595 95 1 2 CARDINAL cana-4595 96 1 3.2.2 CARDINAL cana-4595 97 1 3 CARDINAL cana-4595 98 1 3.2.3 CARDINAL cana-4595 98 2 legendre ORG cana-4595 98 3 jacobi polynomial-based PERSON cana-4595 99 1 1 CARDINAL cana-4595 99 2 runge PERSON cana-4595 100 1 1074 CARDINAL cana-4595 100 2 32 CARDINAL cana-4595 101 1 9s CARDINAL cana-4595 101 2 2025 DATE cana-4595 102 1 2974 2 DATE cana-4595 102 2 legendre ORG cana-4595 103 1 3 CARDINAL cana-4595 103 2 jacobi PERSON cana-4595 104 1 4 CARDINAL cana-4595 104 2 non-linear ORG cana-4595 104 3 4 CARDINAL cana-4595 105 1 3.3 CARDINAL cana-4595 105 2 3.3.1 CARDINAL cana-4595 106 1 1 CARDINAL cana-4595 108 1 the weierstrass approximation theorem ORG cana-4595 110 1 2(π‘₯)𝑑π‘₯ CARDINAL cana-4595 111 1 3.3.2 CARDINAL cana-4595 111 2 2 CARDINAL cana-4595 112 1 5 CARDINAL cana-4595 113 1 4 CARDINAL cana-4595 113 2 non-linear ORG cana-4595 113 3 4.1 CARDINAL cana-4595 114 1 non-linear ORG cana-4595 115 1 caputo PERSON cana-4595 115 2 riemann-liouville PERSON cana-4595 115 3 𝑦(π‘₯ ORG cana-4595 116 1 𝑦(π‘₯ ORG cana-4595 118 1 𝑦(π‘₯ ORG cana-4595 119 1 β€’ CARDINAL cana-4595 121 1 𝑐𝑛]𝑇 ORG cana-4595 122 1 1074 CARDINAL cana-4595 122 2 32 CARDINAL cana-4595 123 1 9s CARDINAL cana-4595 123 2 2025 DATE cana-4595 123 3 2975 β€’ DATE cana-4595 126 1 𝑦(π‘₯))π‘š β‰ˆ βˆ‘ PERSON cana-4595 126 2 π‘‘π‘˜πΊπ‘˜(π‘₯ DATE cana-4595 126 3 π‘‘π‘˜πΊπ‘˜(π‘₯ DATE cana-4595 129 1 newton ORG cana-4595 130 1 4.3 CARDINAL cana-4595 131 1 𝑦(π‘₯ ORG cana-4595 131 2 the gnocchi polynomial approximation ORG cana-4595 131 3 𝑦(π‘₯ ORG cana-4595 133 1 1 CARDINAL cana-4595 133 2 𝑦(π‘₯ ORG cana-4595 135 1 β‰ˆ CARDINAL cana-4595 135 2 𝐿2 CARDINAL cana-4595 135 3 2 ≀ QUANTITY cana-4595 136 1 1074 CARDINAL cana-4595 136 2 32 CARDINAL cana-4595 137 1 9s CARDINAL cana-4595 137 2 2025 DATE cana-4595 137 3 2976 CARDINAL cana-4595 139 1 𝜌(𝑃(𝛼 ORG cana-4595 139 2 𝜌(𝑃(𝛼 ORG cana-4595 141 1 5 CARDINAL cana-4595 141 2 5.1 CARDINAL cana-4595 141 3 legendre ORG cana-4595 141 4 jacobi ORG cana-4595 143 1 legendre polynomial-based ORG cana-4595 145 1 legendre ORG cana-4595 147 1 legendre GPE cana-4595 147 2 β€’ CARDINAL cana-4595 148 1 β€’ CARDINAL cana-4595 149 1 β€’ CARDINAL cana-4595 151 1 5.1.2 CARDINAL cana-4595 153 1 β€’ CARDINAL cana-4595 154 1 β€’ CARDINAL cana-4595 155 1 β€’ CARDINAL cana-4595 157 1 5.1.3 CARDINAL cana-4595 157 2 jacobi polynomial-based PERSON cana-4595 158 1 𝐽𝑛 PERSON cana-4595 158 2 legendre ORG cana-4595 159 1 1074 CARDINAL cana-4595 159 2 32 CARDINAL cana-4595 160 1 9s CARDINAL cana-4595 160 2 2025 DATE cana-4595 161 1 2977 CARDINAL cana-4595 161 2 jacobi polynomial-based PERSON cana-4595 161 3 β€’ CARDINAL cana-4595 163 1 β€’ CARDINAL cana-4595 165 1 5.2 CARDINAL cana-4595 165 2 5.2.1 CARDINAL cana-4595 165 3 legendre ORG cana-4595 166 1 β€’ CARDINAL cana-4595 167 1 β€’ CARDINAL cana-4595 168 1 𝑝0,0 ORG cana-4595 169 1 0 CARDINAL cana-4595 169 2 𝑝2,2 PERSON cana-4595 170 1 5.2.3 CARDINAL cana-4595 170 2 the gnocchi polynomial-based ORG cana-4595 170 3 β€’ CARDINAL cana-4595 171 1 β€’ CARDINAL cana-4595 172 1 β€’ CARDINAL cana-4595 173 1 non-linear ORG cana-4595 174 1 5.3 CARDINAL cana-4595 174 2 gnocchi polynomial ORG cana-4595 177 1 two CARDINAL cana-4595 180 1 one CARDINAL cana-4595 180 2 1074 CARDINAL cana-4595 180 3 32 CARDINAL cana-4595 182 1 9s CARDINAL cana-4595 182 2 2025 DATE cana-4595 183 1 2978 CARDINAL cana-4595 187 1 6 CARDINAL cana-4595 187 2 6.1 CARDINAL cana-4595 190 1 𝑦(π‘₯ ORG cana-4595 191 1 β€’ CARDINAL cana-4595 193 1 β€’ CARDINAL cana-4595 194 1 6.1.1 CARDINAL cana-4595 195 1 the gnocchi polynomial-based ORG cana-4595 196 1 1 CARDINAL cana-4595 197 1 1 CARDINAL cana-4595 197 2 the gnocchi polynomial approximation ORG cana-4595 197 3 6.1.2 CARDINAL cana-4595 198 1 2 CARDINAL cana-4595 199 1 1074 CARDINAL cana-4595 199 2 32 CARDINAL cana-4595 200 1 9s CARDINAL cana-4595 200 2 2025 DATE cana-4595 200 3 2979 CARDINAL cana-4595 200 4 2 CARDINAL cana-4595 200 5 gnocchi polynomial approximation 6.1.3 ORG cana-4595 202 1 3 CARDINAL cana-4595 203 1 3 CARDINAL cana-4595 203 2 gnocchi polynomial approximation ORG cana-4595 203 3 6.2 CARDINAL cana-4595 205 1 1074 CARDINAL cana-4595 205 2 32 CARDINAL cana-4595 207 1 9s CARDINAL cana-4595 207 2 2025 DATE cana-4595 211 1 4 CARDINAL cana-4595 211 2 first ORDINAL cana-4595 212 1 4 CARDINAL cana-4595 212 2 first ORDINAL cana-4595 215 1 5 CARDINAL cana-4595 216 1 5 CARDINAL cana-4595 216 2 1074 CARDINAL cana-4595 216 3 32 CARDINAL cana-4595 218 1 9s CARDINAL cana-4595 218 2 2025 DATE cana-4595 219 1 2981 CARDINAL cana-4595 221 1 1 to 3 CARDINAL cana-4595 221 2 legendre ORG cana-4595 222 1 β€’ CARDINAL cana-4595 222 2 β€’ CARDINAL cana-4595 222 3 β€’ CARDINAL cana-4595 224 1 1 CARDINAL cana-4595 225 1 rigi, f., & tajadodi ORG cana-4595 225 2 h. PERSON cana-4595 225 3 2019 DATE cana-4595 227 1 5(5 CARDINAL cana-4595 227 2 134 CARDINAL cana-4595 227 3 2 CARDINAL cana-4595 228 1 medina-ramos ORG cana-4595 228 2 d. NORP cana-4595 228 3 j., & gonzales-torres ORG cana-4595 228 4 2024, september DATE cana-4595 230 1 2024 CARDINAL cana-4595 230 2 congress of argentina ORG cana-4595 230 3 argencon PERSON cana-4595 232 1 3 CARDINAL cana-4595 232 2 r. NORP cana-4595 232 3 pelosi PERSON cana-4595 232 4 s. PERSON cana-4595 232 5 2016 CARDINAL cana-4595 233 1 1992 DATE cana-4595 233 2 13th ORDINAL cana-4595 233 3 212 CARDINAL cana-4595 234 1 firenze university press ORG cana-4595 235 1 4 CARDINAL cana-4595 235 2 castiglioni PERSON cana-4595 235 3 a. PERSON cana-4595 235 4 2019 DATE cana-4595 237 1 10 CARDINAL cana-4595 237 2 115 CARDINAL cana-4595 238 1 5 CARDINAL cana-4595 238 2 a. PERSON cana-4595 238 3 2023 CARDINAL cana-4595 241 1 politecnico di torino PERSON cana-4595 242 1 6 CARDINAL cana-4595 242 2 giliberti PERSON cana-4595 242 3 2020 DATE cana-4595 244 1 7 CARDINAL cana-4595 244 2 honkapohja ORG cana-4595 244 3 s., & mcclung ORG cana-4595 244 4 n. PERSON cana-4595 244 5 2024 CARDINAL cana-4595 245 1 ssrn 4021712 EVENT cana-4595 246 1 8 CARDINAL cana-4595 246 2 ramos PERSON cana-4595 246 3 h. s. d. c. f. ( PERSON cana-4595 246 4 2018 DATE cana-4595 247 1 three CARDINAL cana-4595 248 1 de coimbra PERSON cana-4595 248 2 portugal GPE cana-4595 249 1 9 CARDINAL cana-4595 249 2 capineri ORG cana-4595 249 3 l. PERSON cana-4595 249 4 2021 CARDINAL cana-4595 251 1 nanomed-2021 DATE cana-4595 252 1 28-28 CARDINAL cana-4595 253 1 mdpi PERSON cana-4595 254 1 10 CARDINAL cana-4595 254 2 danilatou GPE cana-4595 254 3 a. s. i. l. i. k. i. PERSON cana-4595 254 4 2021 CARDINAL cana-4595 256 1 bournemouth university ORG cana-4595 257 1 11 CARDINAL cana-4595 257 2 mccomb PERSON cana-4595 257 3 m. c. PERSON cana-4595 257 4 2020 DATE cana-4595 259 1 university of new york ORG cana-4595 259 2 buffalo GPE