Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808811120210421Investigation the boundary and initial value problems including fractional
integro-differential equations with singular kernelsInvestigation the boundary and initial value problems including fractional
integro-differential equations with singular kernels971081675410.22055/jamm.2021.34670.1848FAMohammadhossein DerakhshanDepartment of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, IranMohammad JahanshahiFaculty of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranHamdam Kazemi DemnehFaculty of Mathematics, Azarbaijan Shahid Madani University Tabriz, IranJournal Article20200817In this paper, the initial and boundary value problems which includes singular fractional integro-differential equations, are investigated. The fractional derivative which is considered in this article, is the Caputo fractional derivative. The integral equations which are discussed in this paper either without any singularity or contain singular kernels that can be weak or strong. In addition to, in this paper to check and study the singularity and regularity of this type of integral equations are paid. Also, the given integral equations are in the form of initial and boundary value problems, which are discussed in terms of the number and manner of boundary conditions. Finally, some examples are provided for the accuracy and efficiency of the method.In this paper, the initial and boundary value problems which includes singular fractional integro-differential equations, are investigated. The fractional derivative which is considered in this article, is the Caputo fractional derivative. The integral equations which are discussed in this paper either without any singularity or contain singular kernels that can be weak or strong. In addition to, in this paper to check and study the singularity and regularity of this type of integral equations are paid. Also, the given integral equations are in the form of initial and boundary value problems, which are discussed in terms of the number and manner of boundary conditions. Finally, some examples are provided for the accuracy and efficiency of the method.https://jamm.scu.ac.ir/article_16754_c6167c953d970a9477df00345a912ce1.pdf