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Inverse problem for a space‐time fractional diffusion equation: Application of fractional Sturm‐Liouville operator
Author(s) -
Ali Muhammad,
Aziz Sara,
Malik Salman A.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4776
Subject(s) - mathematics , fractional calculus , eigenfunction , sturm–liouville theory , uniqueness , mathematical analysis , diffusion equation , operator (biology) , mittag leffler function , inverse , space (punctuation) , inverse problem , boundary value problem , eigenvalues and eigenvectors , philosophy , biochemistry , physics , chemistry , economy , geometry , linguistics , repressor , transcription factor , economics , gene , service (business) , quantum mechanics
An inverse problem of determining a time‐dependent source term from the total energy measurement of the system (the over‐specified condition) for a space‐time fractional diffusion equation is considered. The space‐time fractional diffusion equation is obtained from classical diffusion equation by replacing time derivative with fractional‐order time derivative and Sturm‐Liouville operator by fractional‐order Sturm‐Liouville operator. The existence and uniqueness results are proved by using eigenfunction expansion method. Several special cases are discussed, and particular examples are provided.