Inverse problem for a space‐time fractional diffusion equation: Application of fractional Sturm‐Liouville operator. (2nd February 2018)

• Record Type: Journal Article
• Authors: Ali, Muhammad; Aziz, Sara; Malik, Salman A.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 7(2018)
• Page Start: 2733
• Page End: 2747
• Publication Date: 2018-02-02
• Subjects: fractional derivative -- Mittag‐Leffler function -- Sturm‐Liouville operator; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4776
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.