Abstract
AbstractBy 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.
Funder
Princess Nourah Bint Abdulrahman University
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference36 articles.
1. Isaacs, G.: Exponential laws for fractional differences. Math. Comput. 35(151), 933–936 (1980)
2. Podlubny, I.: Matrix approach to discrete fractional calculus. Fract. Calc. Appl. Anal. 3(4), 359–386 (2000)
3. Khan, Z.: Hadamard type fractional differential equations for the system of integral inequalities on time scales. Integral Transforms Spec. Funct. 31(5), 412–423 (2020)
4. Heymans, N., Podlubny, I.: Physical interpretation of initial conditions for fractional differential equations with Riemann–Liouville fractional derivatives. Rheol. Acta 45, 765–771 (2006)
5. Khurshid, Y., Khan, M.A., Chu, Y.M., Khan, Z.: Hermite–Hadamard Fejér inequalities for conformal fractional integrals via preinvex functions. J. Funct. Spaces 2019, 1–10 (2019)
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献