On strong singular fractional version of the Sturm–Liouville equation

Boundary value problems

Shahram Rezapour¹  Mehdi Shabibi²  Hashem Parvaneh Masiha³  Akbar Zada⁴ 

[1] Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Department of Mathematics, Islamic Azad University, Mehran Branch, Mehran, Ilam, Iran;Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, 15418, Tehran, Iran;Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan;

关键词: Continuous dependence;    Fractional Sturm–Liouville equation;    Strong singular;    The Caputo derivative;    34A08;    34A38;    35A21;    45G05;   

DOI  :  10.1186/s13661-021-01569-8

来源: Springer

【 摘 要 】

The Sturm–Liouville equation is among the significant differential equations having many applications, and a lot of researchers have studied it. Up to now, different versions of this equation have been reviewed, but one of its most attractive versions is its strong singular version. In this work, we investigate the existence of solutions for the strong singular version of the fractional Sturm–Liouville differential equation with multi-points integral boundary conditions. Also, the continuity depending on coefficients of the initial condition of the equation is examined. An example is proposed to demonstrate our main result.

【 授权许可】

CC BY