On a singular time-fractional order wave equation with Bessel operator and Caputo derivative

Mesloub, Saïd; Bachar, Imed

doi:10.22436/jnsa.010.01.06

Cited by 2 publications

(1 citation statement)

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“…There have been few articles related to nonlinear fractional partial equations that employ the energy inequality method [24]. Furthermore, for partial differential equations with classical order, many results have utilized this method [25][26][27][28]. Motivated by the previous results, the authors studied a nonlocal nonlinear time-fractional order problem.…”

Section: Introductionmentioning

confidence: 99%

Solvability of nonlinear fractional integro-differential equation with nonlocal condition

Aicha

Merad

2021

AJMS

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PurposeThis study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results.Design/methodology/approachThe functional analysis method is the a priori estimate method or energy inequality method.FindingsThe results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions.Research limitations/implicationsThe authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order.Originality/valueThe authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.

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