A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

Abstract

In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

Robust uniform stability criteria for fractional‐order gene regulatory networks with leakage delays

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“…Fractional calculus has gained greater attention in recent years, due to its increasing applications in several fields, such as biology, biophysics, chemistry, and signal processing. Compared with the conventional integer‐order model, fractional‐order systems have infinite memory and more degrees of freedom 16–21 . Because of these advantages, the integration of fractional‐order calculus into the nonlinear dynamical system has gained attention and resulted in several new developments in this domain 22–27 .…”

Solvability Criterion for Fractional q-Integro-Difference System with Riemann-Stieltjes Integrals Conditions

“…This is mainly because the effect of using fractional calculus to solve problems is more practical and efficient than that of classical calculus. Over the years, the BVPs for a system of fractional differential equations have developed rapidly, and numerous mature conclusions have been obtained, which can be referred to the literature [19][20][21][22][23][24][25].…”