On the solvability of a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator
Vijai Kumar Pathak, Lakshmi Narayan Mishra, Vishnu Narayan Mishra
Abstract
In this paper, utilizing the technique of generalized Darbo's fixed‐point theorem associated with measure of noncompactness in Banach space, we analyze the existence of solution for a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator. The existing result was obtained to strengthen the ones mentioned previously in the literature. An example for a class of nonlinear functional integral equations is also presented to validate our main result. Finally, we propose the numerical method formed by the modified homotopy perturbation approach to resolving the problem with acceptable accuracy.
Topics & Concepts
MathematicsNonlinear systemFixed-point theoremOperator (biology)Homotopy analysis methodBanach spaceFractional calculusIntegral equationHomotopy perturbation methodMathematical analysisClass (philosophy)Measure (data warehouse)Applied mathematicsHomotopyPure mathematicsComputer scienceTranscription factorGeneChemistryPhysicsBiochemistryQuantum mechanicsArtificial intelligenceDatabaseRepressorFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods