Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications

Advances in Difference Equations

Aziz Khan¹  Zareen A. Khan²  Fahd Jarad³  Hasib Khan⁴ 

[1] Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, 11586, Riyadh, Saudi Arabia;Department of Mathematics, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia;Department of Mathematics, Çankaya University, Ankara, Turkey;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Shaheed Benazir Bhutto University, Sheringal, 18000 Dir Upper, Khyber Pakhtunkhwa, Pakistan;

关键词: Gronwall inequality;    Fractional difference equation;    Fractional sum inequality;    Discrete fractional difference inequality;    26D15;   

DOI  :  10.1186/s13662-021-03257-4

来源: Springer

【 摘 要 】

By means of ς fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gronwall type inequalities for unknown functions. These inequalities are of a new form comparative with the current writing discoveries up until this point and can be viewed as a supportive strategy to assess the solutions of discrete partial differential equations numerically. We show a couple of employments of the compensated inequalities to reflect the benefits of our work. The main outcomes might be demonstrated by the use of the examination procedure and the approach of the mean value hypothesis.

【 授权许可】

CC BY