id sid eid entity type cana-4138 1 1 1074 CARDINAL cana-4138 1 2 32 CARDINAL cana-4138 2 1 9s CARDINAL cana-4138 2 2 2025 CARDINAL cana-4138 2 3 1303 DATE cana-4138 2 4 rajratna m.a PERSON cana-4138 2 5 kulkarni pramod PERSON cana-4138 2 6 sawana GPE cana-4138 2 7 maharashtra state ORG cana-4138 2 8 india GPE cana-4138 2 9 kamblerajratna2@gmail.com bscience college ORG cana-4138 2 10 nanded GPE cana-4138 2 11 maharashtra state GPE cana-4138 2 12 india GPE cana-4138 3 1 12-01-2025 CARDINAL cana-4138 3 2 15-02-2025 CARDINAL cana-4138 3 3 01-03-2025 CARDINAL cana-4138 6 1 34b05 CARDINAL cana-4138 8 1 1 CARDINAL cana-4138 9 1 volterra PERSON cana-4138 16 1 integro-differentail ORG cana-4138 16 2 1 CARDINAL cana-4138 16 3 2 CARDINAL cana-4138 16 4 3 CARDINAL cana-4138 16 5 𝑓(𝑑 ORG cana-4138 18 1 0 CARDINAL cana-4138 18 2 2 CARDINAL cana-4138 19 1 1074 CARDINAL cana-4138 19 2 32 CARDINAL cana-4138 20 1 9s CARDINAL cana-4138 20 2 2025 CARDINAL cana-4138 20 3 1304 CARDINAL cana-4138 20 4 ∈ ORG cana-4138 22 1 𝐼 Γ— 𝐼 Γ— 𝑋 ORG cana-4138 23 1 4 CARDINAL cana-4138 23 2 a. et PERSON cana-4138 24 1 al PERSON cana-4138 24 2 π‘₯(𝑑 ORG cana-4138 25 1 𝑓(𝑑 ORG cana-4138 27 1 5 CARDINAL cana-4138 27 2 claudia, a. ORG cana-4138 27 3 𝑒(π‘₯ WORK_OF_ART cana-4138 28 1 𝑒(𝑠 GPE cana-4138 28 2 𝑦))𝑑𝑦𝑑𝑠 Ο‰ ORG cana-4138 28 3 0 CARDINAL cana-4138 29 1 0 CARDINAL cana-4138 29 2 0 CARDINAL cana-4138 29 3 Ο‰ ∈ ORG cana-4138 31 1 ahmad et al PERSON cana-4138 32 1 6 CARDINAL cana-4138 32 2 four CARDINAL cana-4138 33 1 wang et al PERSON cana-4138 36 1 0 CARDINAL cana-4138 36 2 0 CARDINAL cana-4138 36 3 1 CARDINAL cana-4138 36 4 𝑒(0 PERSON cana-4138 37 1 0 ≀ MONEY cana-4138 37 2 0 CARDINAL cana-4138 37 3 1 CARDINAL cana-4138 37 4 2 DATE cana-4138 37 5 0 CARDINAL cana-4138 37 6 1 CARDINAL cana-4138 38 1 1 0 CARDINAL cana-4138 38 2 1 0 DATE cana-4138 39 1 π‘‘βˆˆ[0 ORG cana-4138 39 2 1 CARDINAL cana-4138 39 3 π‘‘βˆˆ[0 ORG cana-4138 39 4 1 CARDINAL cana-4138 39 5 ∈ ORG cana-4138 39 6 1 CARDINAL cana-4138 39 7 0 CARDINAL cana-4138 39 8 1 CARDINAL cana-4138 39 9 8 CARDINAL cana-4138 40 1 10 CARDINAL cana-4138 40 2 bragdi, a. et al ORG cana-4138 41 1 𝑓(𝑑 ORG cana-4138 41 2 πœ™π‘’(𝑑 PERSON cana-4138 41 3 1074 CARDINAL cana-4138 41 4 32 CARDINAL cana-4138 42 1 9s CARDINAL cana-4138 42 2 2025 CARDINAL cana-4138 42 3 1305 DATE cana-4138 43 1 𝑒(1 ORG cana-4138 44 1 1 CARDINAL cana-4138 44 2 0 CARDINAL cana-4138 44 3 𝑓 ∢ 𝐼 Γ— ℝ3 ORG cana-4138 45 1 0 CARDINAL cana-4138 45 2 1 CARDINAL cana-4138 45 3 πœ™(𝑒)(𝑑 ORG cana-4138 46 1 ∢ 𝐼 Γ— 𝐼 ORG cana-4138 46 2 0 CARDINAL cana-4138 46 3 1 CARDINAL cana-4138 46 4 𝑠𝑒𝑝 ∫ πœ†(𝑑 ORG cana-4138 46 5 1 0 CARDINAL cana-4138 46 6 l. et al.[11 PERSON cana-4138 47 1 12 CARDINAL cana-4138 47 2 r. NORP cana-4138 47 3 kukarni GPE cana-4138 49 1 𝑓(𝑑 ORG cana-4138 49 2 π‘₯(𝜏 DATE cana-4138 50 1 0 CARDINAL cana-4138 50 2 0 CARDINAL cana-4138 50 3 𝐷𝛼, 𝐷𝛽 GPE cana-4138 51 1 0 CARDINAL cana-4138 51 2 1 CARDINAL cana-4138 52 1 0 CARDINAL cana-4138 53 1 0 CARDINAL cana-4138 53 2 1 CARDINAL cana-4138 53 3 ℝ ORG cana-4138 55 1 πœ†(𝜏 PRODUCT cana-4138 55 2 0 πœ™βˆ— MONEY cana-4138 55 3 πœ†(𝜏 ORG cana-4138 56 1 𝛿(𝜏 PRODUCT cana-4138 57 1 2 CARDINAL cana-4138 59 1 2.1 CARDINAL cana-4138 60 1 1 CARDINAL cana-4138 60 2 0 CARDINAL cana-4138 60 3 2 CARDINAL cana-4138 61 1 ∈ ORG cana-4138 61 2 ∈ ORG cana-4138 61 3 3 CARDINAL cana-4138 62 1 0 CARDINAL cana-4138 62 2 2.2 CARDINAL cana-4138 66 1 β€–π‘₯β€– ORG cana-4138 66 2 ∈ ORG cana-4138 66 3 2.3 CARDINAL cana-4138 66 4 1 CARDINAL cana-4138 67 1 𝑑(π‘₯ PERSON cana-4138 68 1 ∈ ORG cana-4138 68 2 2 CARDINAL cana-4138 68 3 𝑑(π‘₯ PERSON cana-4138 69 1 ∈ ORG cana-4138 69 2 1074 CARDINAL cana-4138 69 3 32 CARDINAL cana-4138 70 1 9s CARDINAL cana-4138 70 2 2025 CARDINAL cana-4138 70 3 1306 CARDINAL cana-4138 70 4 𝑑(π‘₯ PERSON cana-4138 70 5 𝑑(π‘₯ PERSON cana-4138 71 1 ∈ ORG cana-4138 72 1 2.4 CARDINAL cana-4138 73 1 ∈ ORG cana-4138 73 2 lim PERSON cana-4138 73 3 d. NORP cana-4138 73 4 o’regan GPE cana-4138 74 1 13 CARDINAL cana-4138 74 2 14 CARDINAL cana-4138 76 1 15 CARDINAL cana-4138 77 1 2.1 CARDINAL cana-4138 77 2 𝑑(𝑓(π‘₯ PERSON cana-4138 77 3 𝑓(𝑦 GPE cana-4138 79 1 ∈ ORG cana-4138 79 2 16 CARDINAL cana-4138 80 1 2.2 CARDINAL cana-4138 81 1 βŠ† CARDINAL cana-4138 84 1 ∈ ORG cana-4138 84 2 0 CARDINAL cana-4138 84 3 1 CARDINAL cana-4138 84 4 ∈ ORG cana-4138 85 1 many centuries DATE cana-4138 86 1 riemann-liouville ORG cana-4138 86 2 caputo PERSON cana-4138 86 3 17 CARDINAL cana-4138 86 4 18 DATE cana-4138 86 5 19 DATE cana-4138 86 6 20 DATE cana-4138 86 7 21 DATE cana-4138 86 8 22 CARDINAL cana-4138 88 1 zero CARDINAL cana-4138 90 1 rolle GPE cana-4138 90 2 lagrange GPE cana-4138 91 1 r. khalil PERSON cana-4138 92 1 23 CARDINAL cana-4138 93 1 24 CARDINAL cana-4138 93 2 25 DATE cana-4138 93 3 26 CARDINAL cana-4138 97 1 3.1 CARDINAL cana-4138 98 1 ∈ ORG cana-4138 98 2 0 CARDINAL cana-4138 99 1 βˆ’ 𝑒(𝑑 PERSON cana-4138 100 1 1074 CARDINAL cana-4138 100 2 32 CARDINAL cana-4138 101 1 9s CARDINAL cana-4138 101 2 2025 CARDINAL cana-4138 101 3 1307 DATE cana-4138 104 1 3.2 CARDINAL cana-4138 104 2 0 CARDINAL cana-4138 104 3 1 CARDINAL cana-4138 104 4 0 CARDINAL cana-4138 105 1 𝐼𝛼𝑒(𝑑 NORP cana-4138 106 1 3.3 CARDINAL cana-4138 107 1 0 CARDINAL cana-4138 107 2 𝑑(π‘₯ PERSON cana-4138 108 1 1)β€”(2 CARDINAL cana-4138 109 1 π‘‘π›Όβˆ’1𝑑𝑑 CARDINAL cana-4138 111 1 4 CARDINAL cana-4138 112 1 4.1 CARDINAL cana-4138 112 2 1)β€”(2 CARDINAL cana-4138 112 3 1 CARDINAL cana-4138 113 1 𝐼 Γ— 𝐼 β†’ ORG cana-4138 113 2 ℝ2 CARDINAL cana-4138 113 3 ℝ2 CARDINAL cana-4138 115 1 βˆ’ β„Ž(𝑑 PERSON cana-4138 115 2 βˆ’ β„Ž(𝑑 PERSON cana-4138 115 3 𝑑(π‘₯ PERSON cana-4138 115 4 2 CARDINAL cana-4138 117 1 π‘‘π›Όβˆ’1𝑑𝑑 CARDINAL cana-4138 119 1 π‘‘π›Όβˆ’1𝑑𝑑 CARDINAL cana-4138 119 2 𝑦(𝑠))𝑑𝑠 GPE cana-4138 122 1 𝑦(𝑠))𝑑𝑠 GPE cana-4138 122 2 1 CARDINAL cana-4138 122 3 2 CARDINAL cana-4138 123 1 π‘Žβ€–πΉπ‘₯(𝑑 NORP cana-4138 123 2 1074 CARDINAL cana-4138 123 3 32 CARDINAL cana-4138 124 1 9s CARDINAL cana-4138 124 2 2025 CARDINAL cana-4138 124 3 1308 DATE cana-4138 126 1 𝑦0β€– + DATE cana-4138 129 1 𝑦(𝑠))𝑑𝑠 GPE cana-4138 130 1 𝑦(𝑠))𝑑𝑠 GPE cana-4138 130 2 π‘Žβ€–π‘₯0 ORG cana-4138 131 1 𝑦0β€– CARDINAL cana-4138 135 1 𝑦(𝑠))𝑑𝑠 GPE cana-4138 136 1 𝑦(𝑠))𝑑𝑠 GPE cana-4138 140 1 π‘₯(𝑠 PERSON cana-4138 142 1 ∫ ORG cana-4138 142 2 π‘₯(𝑠 PERSON cana-4138 143 1 βˆ’ β„Ž(𝑑 PERSON cana-4138 143 2 π‘Žβ€–π‘₯0 ORDINAL cana-4138 144 1 𝑦0β€– CARDINAL cana-4138 146 1 π‘₯(𝑠 PERSON cana-4138 148 1 ∫ ORG cana-4138 148 2 π‘₯(𝑠 PERSON cana-4138 151 1 π‘₯(𝑠 PERSON cana-4138 154 1 π‘₯(𝑠 PERSON cana-4138 156 1 ∫ ORG cana-4138 156 2 π‘₯(𝑠 PERSON cana-4138 157 1 βˆ’ β„Ž(𝑑 PERSON cana-4138 157 2 0 π‘Ž ∫ π‘‘π›Όβˆ’1 MONEY cana-4138 157 3 ∫ ORG cana-4138 157 4 π‘₯(𝑠 PERSON cana-4138 158 1 𝑦))𝑑𝑠 CARDINAL cana-4138 158 2 ∫ 𝑝2(𝑑 ORG cana-4138 158 3 𝑠)πœ™(𝑑(π‘₯ GPE cana-4138 158 4 𝑦))𝑑𝑠 CARDINAL cana-4138 158 5 0 ≀ ∫ π‘‘π›Όβˆ’1 MONEY cana-4138 158 6 0 CARDINAL cana-4138 159 1 𝑠)πœ™(β€–π‘₯ βˆ’ π‘¦β€–βˆž ORG cana-4138 159 2 0 ≀ ∫ π‘‘π›Όβˆ’1 MONEY cana-4138 160 1 𝑠)πœ™(β€–π‘₯ βˆ’ π‘¦β€–βˆž ORG cana-4138 160 2 1074 CARDINAL cana-4138 160 3 32 CARDINAL cana-4138 161 1 9s CARDINAL cana-4138 161 2 2025 CARDINAL cana-4138 162 1 βˆ’ π‘¦β€–βˆž ORG cana-4138 163 1 0 ≀ πœ™(β€–π‘₯ QUANTITY cana-4138 164 1 lemma 2.1 ORG cana-4138 164 2 1)β€”(2 CARDINAL cana-4138 165 1 5 CARDINAL cana-4138 166 1 1)β€”(2 CARDINAL cana-4138 168 1 + 𝑑2𝑠2π‘₯ 2 DATE cana-4138 169 1 ∈ ORG cana-4138 169 2 1 CARDINAL cana-4138 170 1 𝑑(π‘₯ PERSON cana-4138 172 1 π‘₯(𝑠 PERSON cana-4138 174 1 𝑦(𝑠))| NORP cana-4138 174 2 π‘₯(𝑠 PERSON cana-4138 176 1 𝑦(𝑠))| NORP cana-4138 176 2 + π‘₯𝑠2 2 MONEY cana-4138 176 3 2 CARDINAL cana-4138 177 1 2 | TIME cana-4138 178 1 π‘₯𝑠2 2 PRODUCT cana-4138 178 2 2 CARDINAL cana-4138 178 3 2 | TIME cana-4138 178 4 2 CARDINAL cana-4138 178 5 2 CARDINAL cana-4138 179 1 βˆ— CARDINAL cana-4138 179 2 0 CARDINAL cana-4138 179 3 1 CARDINAL cana-4138 179 4 1 2 CARDINAL cana-4138 180 1 π‘₯(𝑠 PERSON cana-4138 181 1 βˆ’ β„Ž(𝑑 PERSON cana-4138 181 2 𝑦(𝑠))| NORP cana-4138 181 3 π‘₯(𝑠 PERSON cana-4138 182 1 βˆ’ β„Ž(𝑑 PERSON cana-4138 182 2 𝑦(𝑠))| NORP cana-4138 182 3 βˆ— CARDINAL cana-4138 182 4 0 CARDINAL cana-4138 182 5 1]into CARDINAL cana-4138 183 1 1 2 CARDINAL cana-4138 183 2 1 CARDINAL cana-4138 183 3 1 CARDINAL cana-4138 183 4 4.1 CARDINAL cana-4138 185 1 1074 CARDINAL cana-4138 185 2 32 CARDINAL cana-4138 186 1 9s CARDINAL cana-4138 186 2 2025 CARDINAL cana-4138 186 3 1310 DATE cana-4138 187 1 1 CARDINAL cana-4138 188 1 burton t PERSON cana-4138 188 2 new york GPE cana-4138 188 3 1983 DATE cana-4138 189 1 2 CARDINAL cana-4138 190 1 r k PERSON cana-4138 190 2 w. a. benjamin PERSON cana-4138 190 3 menlo park GPE cana-4138 190 4 california GPE cana-4138 190 5 1971 DATE cana-4138 191 1 3 CARDINAL cana-4138 192 1 wazwaz, a. PERSON cana-4138 192 2 linear ORG cana-4138 192 3 beijing GPE cana-4138 192 4 2011 DATE cana-4138 193 1 4 CARDINAL cana-4138 194 1 a. PERSON cana-4138 194 2 18 CARDINAL cana-4138 194 3 299, 2005 DATE cana-4138 195 1 5 CARDINAL cana-4138 196 1 b. PERSON cana-4138 196 2 mathematica PERSON cana-4138 196 3 51 CARDINAL cana-4138 196 4 74 CARDINAL cana-4138 197 1 23β€”30 CARDINAL cana-4138 197 2 2009 DATE cana-4138 198 1 6 CARDINAL cana-4138 199 1 b. ahmad PERSON cana-4138 199 2 s. k. ntouyas PERSON cana-4138 199 3 r. p. agarwal PERSON cana-4138 199 4 a. alsaedi PERSON cana-4138 199 5 2016 DATE cana-4138 199 6 1 CARDINAL cana-4138 199 7 article id 205 LAW cana-4138 199 8 2016 DATE cana-4138 200 1 7 CARDINAL cana-4138 201 1 y. wang PERSON cana-4138 201 2 l. liu PERSON cana-4138 201 3 12 CARDINAL cana-4138 201 4 2017 DATE cana-4138 202 1 1-17 CARDINAL cana-4138 203 1 8 CARDINAL cana-4138 204 1 k. hilal PERSON cana-4138 204 2 l. ibnelazyz PERSON cana-4138 204 3 k. guida PERSON cana-4138 204 4 d. melliani PERSON cana-4138 204 5 switzerland ag ORG cana-4138 204 6 2019 DATE cana-4138 205 1 9 CARDINAL cana-4138 206 1 d. baleanu PERSON cana-4138 206 2 k. ghafarnezhad PERSON cana-4138 206 3 s. rezapour PERSON cana-4138 206 4 three CARDINAL cana-4138 206 5 2019 DATE cana-4138 206 6 1 CARDINAL cana-4138 206 7 article id 153, 2019 LAW cana-4138 207 1 10 CARDINAL cana-4138 207 2 bragdi ORG cana-4138 207 3 a. frioui PERSON cana-4138 207 4 a. guezane lakoud PERSON cana-4138 207 5 non-linear ORG cana-4138 208 1 2020 DATE cana-4138 208 2 1 CARDINAL cana-4138 208 3 article id 418,pp LAW cana-4138 209 1 1-9 CARDINAL cana-4138 210 1 11 CARDINAL cana-4138 210 2 l. ibnelazyz PERSON cana-4138 210 3 k. guida PERSON cana-4138 210 4 k. hilal PERSON cana-4138 211 1 melliani PERSON cana-4138 211 2 nonlinear fractional integro-differential ORG cana-4138 211 3 40 DATE cana-4138 211 4 1 CARDINAL cana-4138 211 5 article 33, 2021 LAW cana-4138 212 1 12 CARDINAL cana-4138 213 1 r. m. PERSON cana-4138 213 2 kulkarni PERSON cana-4138 213 3 r. NORP cana-4138 213 4 12(1 CARDINAL cana-4138 213 5 2023 CARDINAL cana-4138 214 1 13 CARDINAL cana-4138 215 1 d. r. smart PERSON cana-4138 215 2 theorems GPE cana-4138 215 3 cambridge university press ORG cana-4138 215 4 1980 DATE cana-4138 216 1 14 CARDINAL cana-4138 217 1 d. o’regan PERSON cana-4138 217 2 cambridge university press ORG cana-4138 217 3 cambridge GPE cana-4138 218 1 15 CARDINAL cana-4138 219 1 huang long-guang PERSON cana-4138 219 2 zhang xian PERSON cana-4138 219 3 332 CARDINAL cana-4138 219 4 1468β€”1476, 2007 DATE cana-4138 220 1 16 CARDINAL cana-4138 221 1 341 CARDINAL cana-4138 221 2 876, 2008 DATE cana-4138 222 1 17 CARDINAL cana-4138 223 1 k. oldham PERSON cana-4138 223 2 j. spanier PERSON cana-4138 223 3 academic press, usa, 1974 ORG cana-4138 224 1 18 CARDINAL cana-4138 225 1 k. s. miller PERSON cana-4138 225 2 b. ross PERSON cana-4138 225 3 wiley-interscience publications, usa ORG cana-4138 225 4 1993 DATE cana-4138 226 1 19 CARDINAL cana-4138 227 1 new york GPE cana-4138 227 2 usa 1999 DATE cana-4138 228 1 1074 CARDINAL cana-4138 228 2 32 CARDINAL cana-4138 229 1 9s CARDINAL cana-4138 229 2 2025 CARDINAL cana-4138 229 3 1311 CARDINAL cana-4138 230 1 20 CARDINAL cana-4138 230 2 r. hilfer PERSON cana-4138 230 3 singapore GPE cana-4138 230 4 2000 DATE cana-4138 231 1 21 CARDINAL cana-4138 232 1 kilbas ORG cana-4138 232 2 h. srivastava PERSON cana-4138 232 3 j. trujillo PERSON cana-4138 232 4 204, 2006 DATE cana-4138 233 1 22 CARDINAL cana-4138 234 1 t. zhou PERSON cana-4138 234 2 xiangtan university ORG cana-4138 234 3 china GPE cana-4138 234 4 2014 DATE cana-4138 235 1 23 CARDINAL cana-4138 236 1 r. khalil PERSON cana-4138 236 2 m. al horani PERSON cana-4138 236 3 a. yousef PERSON cana-4138 236 4 m. sababheh PERSON cana-4138 236 5 264 CARDINAL cana-4138 236 6 6570, 2014 DATE cana-4138 237 1 24 CARDINAL cana-4138 238 1 t. abdeljawad PERSON cana-4138 238 2 279 CARDINAL cana-4138 238 3 5766 DATE cana-4138 238 4 10.1016 CARDINAL cana-4138 238 5 j.cam.2014.10.016 ORG cana-4138 238 6 2015 DATE cana-4138 239 1 25 CARDINAL cana-4138 240 1 t. abdeljawad PERSON cana-4138 240 2 m. al horani PERSON cana-4138 240 3 r. khalil PERSON cana-4138 240 4 2015 DATE cana-4138 240 5 2015 DATE cana-4138 241 1 26 CARDINAL cana-4138 242 1 r. NORP cana-4138 242 2 kulkarni PERSON cana-4138 242 3 3026β€”3033 CARDINAL cana-4138 242 4 2024 CARDINAL