Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
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Choukri Derbazi
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Zidane Baitiche
Abstract
This manuscript is committed to deal with the existence and uniqueness of positive solutions for fractional relaxation equation involving ψ-Caputo fractional derivative. The existence of solution is carried out with the help of Schauder’s fixed point theorem, while the uniqueness of the solution is obtained by applying the Banach contraction principle, along with Bielecki type norm. Moreover, two explicit monotone iterative sequences are constructed for the approximation of the extreme positive solutions to the proposed problem. Lastly, two examples are presented to support the obtained results.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
- Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
- Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
- On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
- On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
- A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
- Solitary waves of the RLW equation via least squares method
- Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber
- Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces
- Modified inertial subgradient extragradient method for equilibrium problems
- Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
- Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
- Investigation of nonlinear fractional delay differential equation via singular fractional operator
- Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions
- The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions
- Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
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