بررسی مسایل مقدار مرزی و اولیه شامل معادلات انتگرو دیفرانسیل کسری با هسته‌های تکینی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی صنایع، موسسه آموزش عالی آپادانا، شیراز، ایران

2 گروه ریاضی، دانشکده علوم پایه، دانشگاه شهید مدنی آذر بایجان، تبریز، ایران

چکیده

در این ﻣﻘﺎﻟﻪ مسایل ﻣﻘﺪار اولیه و ﻣﺮزی ﮐﻪ ﺷﺎﻣﻞ ﻣﻌﺎدﻻت اﻧﺘﮕﺮو دیفرانسیل غیرﻋﺎدی ﮐﺴﺮی است، ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮار می‌گیرد. مشتق کسری که در این مقاله درنظر گرفته شده است، مشتق کسری کپوتو است. ﻣﻌﺎدﻻت اﻧﺘﮕﺮاﻟﯽ ﮐﻪ در این ﻣﻘﺎﻟﻪ مورد بررسی قرار می‌گیرند یا بدون هرگونه تکینی‌اند و یا شامل هسته‌های تکینی‌اند که این تکینی می‌تواند ضعیف یا قوی باشد. به‌علاوه در این مقاله به بررسی و مطالعه رفع تکینی و منظم‌سازی این نوع از معادلات انتگرالی پرداخته می‌شود. هم‌چنین ﻣﻌﺎدﻻت اﻧﺘﮕﺮالی داده‌شده در ﻗﺎﻟﺐ مسایل ﻣﻘﺪار مرزی و اولیه ﺑﻮده ﮐﻪ در این مسایل از ﻧﻈﺮ ﺗﻌﺪاد و چگونگی شرایط ﻣﺮزی ﻣﻮرد ﺑﺤﺚ ﻗﺮار می‌گیرند. در پایان برای صحت و کارایی روش، بعضی مثال‌ها ارائه شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Investigation the boundary and initial value problems including fractional integro-differential equations with singular kernels

نویسندگان [English]

  • Mohammadhossein Derakhshan 1
  • Mohammad Jahanshahi 2
  • hamdam kazemi demneh 2
1 Department of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran
2 Faculty of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
چکیده [English]

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.

کلیدواژه‌ها [English]

  • fractional integro-differential equation
  • singular
  • weak singularity
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