Abstract
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.
Highlights
1 Introduction Fractional calculus consisting of a derivative and an integral component of noninteger order is a natural increase in the regular integer order calculus
With different analysts and experts devoting themselves to this area, fractional analytic is apparently widespread considering its intriguing applications concerning various fields of science, for instance, viscoelasticity, dispersion, nervous system science, control hypothesis, and statistics [1,2,3,4,5,6,7,8,9]
Atici and Eloe [14] explored the layout of a discrete fractional calculus with the nabla operator
Summary
Fractional calculus consisting of a derivative and an integral component of noninteger order is a natural increase in the regular integer order calculus. The justification for this paper is to implement discrete fractional sum equations in terms of creating a method for interpreting such equations and to derive the related Gronwall form of inequality. The discrete counterpart of the hypothesis in the presence of a fractional sum of order ς > 0 was described by Miller and Ross [11] who discussed solutions to linear difference equation and checked some basic features of this operator. Atici and Eloe [14] explored the layout of a discrete fractional calculus with the nabla operator. They generated exponential laws and the item rule for the forward fractional calculus. The last bit is considered in fulfilling the theoretical examination necessities
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