QUALITATIVE PROPERTIES OF SOLUTIONS OF FRACTIONAL DIFFERENTIAL AND DIFFERENCE EQUATIONS ARISING IN PHYSICAL MODELS

Zareen A. Khan and Hijaz Ahmad
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Zareen A. Khan: Department of Mathematics, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
Hijaz Ahmad: ��Department of Basic Sciences, University of Engineering and Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan‡Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-10

Abstract: Discrete fractional calculus (DFC) is suggested to interpret neural schemes with memory impacts. This study seeks to formulate some discrete fractional nonlinear inequalities with ξ̂ fractional sum operators that are used with some conventional and forthright inequalities. Taking into consideration, we recreate the explicit bounds of Gronwall-type inequalities by observing the principle of DFC for unknown functions here. Such inequalities are of new version relative to the current literature findings so far and can be used as a helpful method to evaluate the numerical solutions of discrete fractional differential equations. We show a few uses of the rewarded inequalities to mirror the advantages of our work. Regarding applications, we can apply the acquainted results to discuss boundedness, uniqueness, and continuous dependency on the initial value problem for the solutions of certain underlying worth problems of fractional difference equations. The leading consequences may be proven by the usage of the analysis process and the methodology of the mean value theorem. These variations can be used as an advantageous device in the subjective examination solutions of discrete fractional difference equations.

Keywords: Fractional Sum Inequality; Gronwall Inequality; Discrete Fractional Difference Inequality; Fractional Difference Equation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21400247

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