Gene

Banach space

Fixed-point theorem

Functional analysis

Differential equation

Linear differential equation

Applied mathematics

Stability (learning theory)

Biochemistry

Computer science

Contraction (grammar)

Contraction mapping

Mathematics

Internal medicine

Transcription factor

Mathematical analysis

Ordinary differential equation

Uniqueness

Repressor

Medicine

Chemistry

C0-semigroup

Partial differential equation

Operator (biology)

Fractional calculus

Contraction principle

Machine learning

Advances in Difference Equations

In this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Laplacian operator. Also we investigate the Hyers–Ulam (HU) stability of solutions. For the existence result, we establish the integral form of the FDE by using the Green function and then the existence of a solution is obtained by applying Guo–Krasnoselskii’s fixed point theorem. For our purpose, we also check the properties of the Green function. The uniqueness of the result is established by applying the Banach contraction mapping principle. An example is offered to ensure the validity of our results.

On stability analysis and existence of positive solutions for a general non-linear fractional differential equations