Intermediate value problems for fractional differential equations

Yang, Guang; Shiri, Babak; Kong, Hua; Wu, Guo–Cheng

doi:10.1007/s40314-021-01590-8

Cited by 19 publications

(13 citation statements)

References 22 publications

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“…A similar argument shows that D Tn (a, f ) for a ∈ (−∞, f i1 ] takes its minimum on a = f i1 and D Tn (a, f ) for a ∈ [f in , ∞) takes its minimum on f in . Conclusively, (8) holds and this completes the proof.…”

Section: Average Distancesupporting

confidence: 61%

“…It is known that for solving diverse operator equation with Galerkin or collocation method the error will be proportional to the approximation error [1]. Of recent analysis, we can observe these proportional in error in collocation methods for solving fractional differential equations and related inverse problems [2,6,8]. Therefore, it is important before using these methods for solving diverse operator equation, we have some views about divergence and convergence of resolution approximations.…”

Section: Introductionmentioning

confidence: 99%

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Resolution approximation method; An analysis, failures and successes

Shiri

2022

Preprint

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The resolution approximation method is introduced for the first time for data approximating with minimizing an energy function. The minimization problem of the corresponding energy function is analyzed with three different distances, maximum distance, average distance and Ecleadian distance. Interestingly, the first approximations for monomials with introduced distances are equivalent to descriptive statistics such as minimum, maximum, average and median. Unfortunately, the resolution approximation methods with monomials fail. A cure with Haar scale functions is introduced. The theoretical results are validated with some examples. MSC Classification: 41A05 , 94A16

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Section: Average Distancesupporting

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Resolution approximation method; An analysis, failures and successes

Shiri

2022

Preprint

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“…Function. The use of non-integer operators has appeared recently in various technical [59][60][61] and science specialties [17][18][19]. For instance, the fractional kinetic equation is useful in studying gas theory, astrophysics, and aerodynamics [62][63][64].…”

Section: Pathway Transforms and The Solution Of Fractional Kinetic Eq...mentioning

confidence: 99%

“…by using the Riemann-Liouville (R-L) fractional integral ( I δ 0+ , δ > 0). We now formulate and solve the fractional kinetic equation, as proposed by Haubold and Mathai [59] i-e for any integrable function f ðtÞ:…”

Section: Pathway Transforms and The Solution Of Fractional Kinetic Eq...mentioning

confidence: 99%

Unified Approach to Fractional Calculus Images Involving the Pathway Transform of Extendedk-Gamma Function and Applications

Tassaddiq

Nantomah²

2022

Advances in Mathematical Physics

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A path way model is concerned with the rules of swapping among different classes of functions. Such model is significant to fit a parametric class of distributions for new data. Based on a such model, the path way or P δ transform is of binomial type and contains a family of different transforms. Taking inspiration from these facts, present research is concerned with the computation of new fractional calculus images involving the extended k -gamma function. The non-integer kinetic equations containing the extended k -gamma function is solved by using pathway transform as well as validated with the earlier obtained results. P δ transform of Dirac delta function is obtained which proved useful to achieve the purpose. As customary, the results for the frequently used Laplace transform can be recovered by taking δ ⟶ 1 in the definition of P δ transform. Important new identities involving the Fox-Wright function are obtained and used to simplify the results. It is remarkable that the several new and novel results involving the classical gamma function became possible by using this approach.

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“…Existences of terminal value problems (TVPs) of fractional differential equations [2-4, 10, 14] were investigated and applications were suggested in [6,15,16]. A linear -dimensional TVP for a general fractional system (GFS) is described by where C D ,g a+ (0 < 𝛼 ≤ 1) is the general fractional derivative (see Definition 3), f ∶ [a, b] → ℝ is a source function (or external force), A is a × coefficient matrix and y(b) = T ∈ ℝ is a terminal value.…”

Section: Introductionmentioning

confidence: 99%

Terminal Value Problems of Non-homogeneous Fractional Linear Systems with General Memory Kernels

Shiri

Fan

et al. 2022

J Nonlinear Math Phys

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Terminal value problems of fractional linear systems with non-homegenous terms are investigated in this paper for the first time. They are equivalent to a second kind weakly singular Volterra–Fredholm integral system. Picard’s method is used to obtain a closed form solution. The exact solution is checked to satisfy the terminal value problem. Numerical solutions are provided in comparison with truncated exact ones.

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Intermediate value problems for fractional differential equations

Cited by 19 publications

References 22 publications

Resolution approximation method; An analysis, failures and successes

Resolution approximation method; An analysis, failures and successes

Unified Approach to Fractional Calculus Images Involving the Pathway Transform of Extendedk-Gamma Function and Applications

Terminal Value Problems of Non-homogeneous Fractional Linear Systems with General Memory Kernels

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