Abstract
The present work focuses on entropy solutions for the fractional Cauchy problem of nonsymmetric systems. We impose sufficient conditions on the parameters to obtain bounded solutions of L∞ . The solutions attained are unique and exclusive. Performance is established by utilizing the maximum principle for certain generalized time and space-fractional diffusion equations. The fractional differential operator is inspected based on the interpretation of the Riemann–Liouville differential operator. Fractional entropy inequalities are imposed.
Highlights
Fractional order differential equations have been positively engaged in modeling of various different procedures and schemes in engineering, physics, chemistry, biology, medicine, and food processing [1,2,3,4]
Fractional calculus created from the Riemann–Liouville description of fractional integral of order ℘ is in the form
Alsaedi et al [15] presented an inequality for fractional derivatives related to the Leibniz rule, as follows: Lemma 1
Summary
Fractional order differential equations have been positively engaged in modeling of various different procedures and schemes in engineering, physics, chemistry, biology, medicine, and food processing [1,2,3,4]. In these requests, reflecting boundary value problems such as the existence and uniqueness of solutions for space-time fractional diffusion equations on bounded domains is a significant procedure. Alsaedi et al [15] presented an inequality for fractional derivatives related to the Leibniz rule, as follows: Lemma 1. Various studies have discussed the fractional Cauchy problem [17,18] and entropy analysis [19,20,21]
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