FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND Ψ–HILFER FRACTIONAL DERIVATIVE
Copyright policy )FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND Ψ–HILFER FRACTIONAL DERIVATIVE
Considering a fractional integro-differential equation with nonlocal conditions involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem and Krasnoselskii's fixed point theorem. An example is provided to illustrate our main results.
- Hodeidah University Yemen
- South Valley University Egypt
- South Valley University Zambia
- Dr. Babasaheb Ambedkar Marathwada University India
fixed point theorem, least squares method, Differential equation, Mittag-Leffler function, Fractional derivatives and integrals, Banach fixed-point theorem, Stability (learning theory), Integral equations, Mittag-Leffler function, Ecology, fractional integro-differential equations, Applied Mathematics, Statistics, Articles, fractional integro-differential equations, Stability of Functional Equations in Mathematical Analysis, \(\psi\)-fractional integral, Fractional Derivatives, ψ -Hilfer fractional derivative, Picard–Lindelöf theorem, Modeling and Simulation, Physical Sciences, Exponential sums, Spectral, collocation and related methods for boundary value problems involving PDEs, Uniqueness, Type (biology), Fractional Differential Equations, Variety (cybernetics), fixed point theorem, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Fixed-point theorems, Machine learning, QA1-939, FOS: Mathematics, existence and and Ulam-Hyers stability, ψ-fractional integral, Fixed-point theorem, Functional Differential Equations, Biology, Anomalous Diffusion Modeling and Analysis, Banach space, Time-Fractional Diffusion Equation, Fractional calculus, Applied mathematics, Computer science, FOS: Biological sciences, Fractional Calculus, \(\psi\)-Hilfer fractional derivative, Mathematics
fixed point theorem, least squares method, Differential equation, Mittag-Leffler function, Fractional derivatives and integrals, Banach fixed-point theorem, Stability (learning theory), Integral equations, Mittag-Leffler function, Ecology, fractional integro-differential equations, Applied Mathematics, Statistics, Articles, fractional integro-differential equations, Stability of Functional Equations in Mathematical Analysis, \(\psi\)-fractional integral, Fractional Derivatives, ψ -Hilfer fractional derivative, Picard–Lindelöf theorem, Modeling and Simulation, Physical Sciences, Exponential sums, Spectral, collocation and related methods for boundary value problems involving PDEs, Uniqueness, Type (biology), Fractional Differential Equations, Variety (cybernetics), fixed point theorem, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Fixed-point theorems, Machine learning, QA1-939, FOS: Mathematics, existence and and Ulam-Hyers stability, ψ-fractional integral, Fixed-point theorem, Functional Differential Equations, Biology, Anomalous Diffusion Modeling and Analysis, Banach space, Time-Fractional Diffusion Equation, Fractional calculus, Applied mathematics, Computer science, FOS: Biological sciences, Fractional Calculus, \(\psi\)-Hilfer fractional derivative, Mathematics
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