{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MVW26WE3FE2A7PQS47MJB53T6N","short_pith_number":"pith:MVW26WE3","canonical_record":{"source":{"id":"1510.00408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-26T18:34:07Z","cross_cats_sorted":[],"title_canon_sha256":"70d4720b06048397ede571696ef0521c33f6db82eedbbaaa777d3e325e676544","abstract_canon_sha256":"7e0389309b65e9c129f761729803c41ec107f72bfbc048eadf18712cfd5e0791"},"schema_version":"1.0"},"canonical_sha256":"656daf589b29340fbe12e7d890f773f36133c903adf3c64863544d7f11e0c784","source":{"kind":"arxiv","id":"1510.00408","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00408","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00408v2","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00408","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"MVW26WE3FE2A","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MVW26WE3FE2A7PQS","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MVW26WE3","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MVW26WE3FE2A7PQS47MJB53T6N","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-26T18:34:07Z","cross_cats_sorted":[],"title_canon_sha256":"70d4720b06048397ede571696ef0521c33f6db82eedbbaaa777d3e325e676544","abstract_canon_sha256":"7e0389309b65e9c129f761729803c41ec107f72bfbc048eadf18712cfd5e0791"},"schema_version":"1.0"},"canonical_sha256":"656daf589b29340fbe12e7d890f773f36133c903adf3c64863544d7f11e0c784","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:26.483889Z","signature_b64":"zl7qCmNKsUOoPsq06T2ITzHZZ3OZPg2Jx/rl/6HLAN3r6Vgv4E+DmgsqSWrk+TS07FF57hPEbhd+GP4S83Z7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"656daf589b29340fbe12e7d890f773f36133c903adf3c64863544d7f11e0c784","last_reissued_at":"2026-05-18T00:59:26.483256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:26.483256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00408","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PSmzHpr2pkZrSPNl8aZbJNzL67yv9CAo8phUCE+ogdMoAsUVhTj5jG7FAmvm4Oy9lhJP4GgpwEOeRzPm2WT6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:51:17.428333Z"},"content_sha256":"2831b62cf2c300a65a766344a939bb95344c539fbbbc4511870817802370a6da","schema_version":"1.0","event_id":"sha256:2831b62cf2c300a65a766344a939bb95344c539fbbbc4511870817802370a6da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MVW26WE3FE2A7PQS47MJB53T6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"David A. Edwards, Ryan M. Evans, Udita N. Katugampola","submitted_at":"2015-09-26T18:34:07Z","abstract_excerpt":"In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by employing techniques from fractional calculus; several examples are discussed. Furthermore, for the first time, we encounter an order of the fractional derivative other than $\\frac{1}{2}$ in an applied problem. Hence, in this paper we explore the applicability of fractional calculus in real-world applications, further strengthening the true nature of fractional c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00408","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pUUPxF0lLUXLIzRlTOti+4gNID3jPCGl4dQaXNMpZdFACTp9m/aJ8+2VYvpo0fuKNYt4QvcHEdOm02fy/EMaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:51:17.428981Z"},"content_sha256":"9c131e6bb97a3a6ea4d602d1db7f1e0b282f141a37e66a21a39d37f8db19184d","schema_version":"1.0","event_id":"sha256:9c131e6bb97a3a6ea4d602d1db7f1e0b282f141a37e66a21a39d37f8db19184d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVW26WE3FE2A7PQS47MJB53T6N/bundle.json","state_url":"https://pith.science/pith/MVW26WE3FE2A7PQS47MJB53T6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVW26WE3FE2A7PQS47MJB53T6N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T13:51:17Z","links":{"resolver":"https://pith.science/pith/MVW26WE3FE2A7PQS47MJB53T6N","bundle":"https://pith.science/pith/MVW26WE3FE2A7PQS47MJB53T6N/bundle.json","state":"https://pith.science/pith/MVW26WE3FE2A7PQS47MJB53T6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVW26WE3FE2A7PQS47MJB53T6N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MVW26WE3FE2A7PQS47MJB53T6N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7e0389309b65e9c129f761729803c41ec107f72bfbc048eadf18712cfd5e0791","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-26T18:34:07Z","title_canon_sha256":"70d4720b06048397ede571696ef0521c33f6db82eedbbaaa777d3e325e676544"},"schema_version":"1.0","source":{"id":"1510.00408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00408","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00408v2","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00408","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"MVW26WE3FE2A","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MVW26WE3FE2A7PQS","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MVW26WE3","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:9c131e6bb97a3a6ea4d602d1db7f1e0b282f141a37e66a21a39d37f8db19184d","target":"graph","created_at":"2026-05-18T00:59:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by employing techniques from fractional calculus; several examples are discussed. Furthermore, for the first time, we encounter an order of the fractional derivative other than $\\frac{1}{2}$ in an applied problem. Hence, in this paper we explore the applicability of fractional calculus in real-world applications, further strengthening the true nature of fractional c","authors_text":"David A. Edwards, Ryan M. Evans, Udita N. Katugampola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-26T18:34:07Z","title":"Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00408","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2831b62cf2c300a65a766344a939bb95344c539fbbbc4511870817802370a6da","target":"record","created_at":"2026-05-18T00:59:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7e0389309b65e9c129f761729803c41ec107f72bfbc048eadf18712cfd5e0791","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-26T18:34:07Z","title_canon_sha256":"70d4720b06048397ede571696ef0521c33f6db82eedbbaaa777d3e325e676544"},"schema_version":"1.0","source":{"id":"1510.00408","kind":"arxiv","version":2}},"canonical_sha256":"656daf589b29340fbe12e7d890f773f36133c903adf3c64863544d7f11e0c784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"656daf589b29340fbe12e7d890f773f36133c903adf3c64863544d7f11e0c784","first_computed_at":"2026-05-18T00:59:26.483256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:26.483256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zl7qCmNKsUOoPsq06T2ITzHZZ3OZPg2Jx/rl/6HLAN3r6Vgv4E+DmgsqSWrk+TS07FF57hPEbhd+GP4S83Z7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:26.483889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2831b62cf2c300a65a766344a939bb95344c539fbbbc4511870817802370a6da","sha256:9c131e6bb97a3a6ea4d602d1db7f1e0b282f141a37e66a21a39d37f8db19184d"],"state_sha256":"727f6a8d71b8352f77aa5d9ae84c0e8b9d8883db0f44cbff7296bc2affdb9ae3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ijFKtxQyH5NwBMVlN8AtT1xQ9GfxqWhQxozAER5SgCtBcDU3XJ0VnZqKeYA5Ja7nZZGyZ37UoGx/23R3wp0ZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:51:17.432172Z","bundle_sha256":"c30c83ffc4fc4cc7a84c233eea3806425b282b264f44db8c0baa2023142d1803"}}